{"group":{"id":1,"name":"Community","lockable":false,"created_at":"2012-01-18T18:02:15.000Z","updated_at":"2026-04-06T14:01:22.000Z","description":"Problems submitted by members of the MATLAB Central community.","is_default":true,"created_by":161519,"badge_id":null,"featured":false,"trending":false,"solution_count_in_trending_period":0,"trending_last_calculated":"2026-04-06T00:00:00.000Z","image_id":null,"published":true,"community_created":false,"status_id":2,"is_default_group_for_player":false,"deleted_by":null,"deleted_at":null,"restored_by":null,"restored_at":null,"description_opc":null,"description_html":null,"published_at":null},"problems":[{"id":57472,"title":"Compute the Lagarias Riemann Hypothesis sequence","description":"Write a function that takes an input number  and produces a sequence (i.e., all values up to and including the th value) computed with \r\n\r\nwhere  is the th harmonic number and  is the sum of divisors of . \r\nLagarias proved that  for all  only if the Riemann Hypothesis is true. ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 132px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 66px; transform-origin: 407px 66px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 135.225px 8px; transform-origin: 135.225px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function that takes an input number \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 203.45px 8px; transform-origin: 203.45px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and produces a sequence (i.e., all values up to and including the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 28.7833px 8px; transform-origin: 28.7833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eth value) computed with \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg 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mQt6v37LKL3fBrpcFsWOUnmWUdNtIgTqK0TIjEZIidqEl+3QfmWPHa+RC+swtX4RYmBxqI3W7Ug8N0Vmp5fwXSyOLvkn3mnXIUUW3/f4mLSvpvrh73ce6kqdUnzt1IrXz3k+ku1YW6/e6D09CywdpKafOvC+Ms39ZGe8XX1qdz163QOBsb4fX8QnNsj4EmtYd4cfulyklBSw/ZL/by4O5AgMHYqP010iwpqOb4ugYL0wjheIfEvkRhE9ECdtLD/D2L4pkjtdVNec8E2lHJPGuXBsNHX4pEjNwWgH8dbc5Oq4ld9FCQxGxOcVIGv2yumKey8V0Q9q2fvBneAXcdzHosu5CYzimeJ8u/yBTEz6ZWGOv1e9cY/tFyW9Mp2kaXJLYNhhxDfK6KdclEd/9LZ/a52xCYL8ZQUbwB5fXrCdtO7cyycqtC7WzqjPHSLWh9i/p/8nmHGYZS74qE/gGYuLLUP9CnX8okjNP0HsWQcE9t7V42Mo91ymYDBhMMYx+dYm9FZ8K39XX2uLoJ/Xpk5q+FHOWelV9ZIbYFqccn8nJn1KhL5zXsSzJUicN+BVTHv0yrN7ITDUNfUt+q2tKHGx9repmO7tEvI6tfd3HeEsPa2DYy8RIa+OW/l7lMCcVX2PQZd0ZD4empKLs8K09b3eWonW8giQbxaprTlpLXOO+wlQZHdbszct79Zp8dxW81w5e/Ixa+DXgjX3aibqnQEC0lq2vZ8s5otEohs5evW6JwIzBc/02U3FgaUJjLI/bx56CsD6pd6owU5515LPbp3ADF0uqf1Y2XMTGN5KFqK2niBWs3nv0qm22pq3KW/UYMr3YCKj0L35mKXx68We4McaSrt4vbes3HOUz0aTKCmdotdTJTCbigNrEBgaDCu+WGTuERUGyw6PdIvqnJ1irbL2QGCGLteyhvx7liAwvIlyz4t4qfk1W68foON7OKWdJr31oZ3p1HiprL36mCXx68Wd55jigjh63/1qfYeStqi9TNXrKROYzcSBtQiMsjbWY8xFYjDAt4nYD1O1Gv2W7t8LgRm6PDurWYrA0CIyMS1rVdZAgaB0g0hpvUtPHViLwe7JCFnbu49ZAr8ezNNndC3TXCRG18jU1gbZOsyh11MnMJuIA2sSGBqModUW1bV0jtzppi3Pb+3ePRGYocuzsR57bkf0gK6Wms7ZP1ve6907Z71a/EbLvV4bzvLvc+I3VzvmrBNlcUVjyxx6HQTmbszn1GOzXtYmMHMZ/zGWk55ybNvIGoXolsBjxObU26Rz9czt64VNkEW4RSSyjuPUMRztHwj0IGDPz0qfj3xguOed45kgAoPABIFa6TZITO66S3459zqAlZo0XjMQGAgMBHaLANNNbHfPXdEjKHbb+K1XfBCYrWto1G8gMBAYCAwEBgIDgf9DYBCYYRQDgYHAQGAgMBAYCOwOgUFgdqeyUeGBwEBgIDAQGAgMBP4LF1UVj20LUicAAAAASUVORK5CYII=\" alt=\"a(n) = floor(H(n) + exp(H(n))ln(H(n)))-sigma(n)\" style=\"width: 280px; height: 18.5px;\" width=\"280\" height=\"18.5\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 21.0083px 8px; transform-origin: 21.0083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ewhere \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"H(n)\" style=\"width: 35.5px; height: 18.5px;\" width=\"35.5\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 20.6083px 8px; transform-origin: 20.6083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 7.775px 8px; transform-origin: 7.775px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eth \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/46000\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eharmonic number\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.5583px 8px; transform-origin: 15.5583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"sigma(n)\" style=\"width: 30.5px; height: 18.5px;\" width=\"30.5\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 20.6083px 8px; transform-origin: 20.6083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/46898\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003esum of divisors\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 9.71667px 8px; transform-origin: 9.71667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 28.7917px 8px; transform-origin: 28.7917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eLagarias \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://arxiv.org/abs/math/0008177\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003eproved\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.55px 8px; transform-origin: 15.55px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e that \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"a(n) \u003e= 0\" style=\"width: 56px; height: 18.5px;\" width=\"56\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 21px 8px; transform-origin: 21px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e for all \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 33.8333px 8px; transform-origin: 33.8333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e only if the \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://en.wikipedia.org/wiki/Riemann_hypothesis\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003eRiemann Hypothesis\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 24.8833px 8px; transform-origin: 24.8833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is true. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function a = LagariasRH(n)\r\n  a = floor(H(n)+exp(H(n))*ln(H(n))-sigma(n);\r\nend","test_suite":"%%\r\nn = 100;\r\ny = LagariasRH(n);\r\ny_correct = [0 0 1 0 4 0 7 2 7 5 13 0 17 9 12 8 23 5 27 8 21 20 34 1 33 25 30 17 46 7 50 22 40 37 46 6 62 43 50 19 70 19 74 37 46 55 82 9 79 46 70 47 95 32 83 38 81 74 107 2 112 81 76 56 102 45 125 70 103 58 133 14 138 101 94 81 129 60 151 48 116 115 160 23 142 122 137 80 173 33 158 105 148 136 163 34 192 122 140 82];\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 1000;\r\ny = LagariasRH(n);\r\nsum_correct = 914917;\r\nnprimes_correct = 155;\r\nassert(isequal(sum(y),sum_correct) \u0026\u0026 isequal(sum(isprime(y)),nprimes_correct))\r\n\r\n%%\r\nn = 10000;\r\ny = LagariasRH(n);\r\ny953_correct = [2461 4261 7113 8116 12978 11195 18980 16294 22215 21474];\r\nassert(isequal(y(953:953:n),y953_correct))\r\n\r\n%%\r\nn = 100000;\r\ny = LagariasRH(n);\r\nsum_correct = 13587430007;\r\nnprimes_correct = 8811;\r\nassert(isequal(sum(y),sum_correct) \u0026\u0026 isequal(sum(isprime(y)),nprimes_correct))\r\n\r\n%%\r\nn = 1000000;\r\ny = LagariasRH(n);\r\ny95395_correct = [308341 521204 855014 963930 1629129 1304492 2221964 1881773 2573303 2750908];\r\nassert(isequal(y(95395:95395:n),y95395_correct))\r\n\r\n%%\r\ny1 = LagariasRH(20403);\r\ny2 = LagariasRH(y1(end));\r\nf  = factor(y2(end));\r\ns3 = sum(LagariasRH(prod(f(end-2:end))));\r\ns3_correct = 350693690;\r\nassert(isequal(s3,s3_correct))\r\n\r\n%%\r\nfiletext = fileread('LagariasRH.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp') || contains(filetext, 'oeis') || contains(filetext, 'persistent'); \r\nassert(~illegal)","published":true,"deleted":false,"likes_count":2,"comments_count":2,"created_by":46909,"edited_by":46909,"edited_at":"2022-12-25T05:52:21.000Z","deleted_by":null,"deleted_at":null,"solvers_count":7,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2022-12-23T23:17:27.000Z","updated_at":"2026-02-03T17:06:47.000Z","published_at":"2022-12-23T23:19:21.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function that takes an input number \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and produces a sequence (i.e., all values up to and including the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003eth value) computed with \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"a(n) = floor(H(n) + exp(H(n))ln(H(n)))-sigma(n)\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea(n) = \\\\lfloor H(n)+\\\\exp(H(n))\\\\ln(H(n))\\\\rfloor - \\\\sigma(n)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"H(n)\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eH(n)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003eth \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/46000\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eharmonic number\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"sigma(n)\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\sigma(n)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/46898\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003esum of divisors\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eLagarias \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://arxiv.org/abs/math/0008177\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eproved\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e that \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"a(n) \u0026gt;= 0\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea(n) \\\\ge 0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e for all \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e only if the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/Riemann_hypothesis\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eRiemann Hypothesis\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e is true. 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","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 132px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 66px; transform-origin: 407px 66px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 135.225px 8px; transform-origin: 135.225px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function that takes an input number \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 203.45px 8px; transform-origin: 203.45px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and produces a sequence (i.e., all values up to and including the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 28.7833px 8px; transform-origin: 28.7833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eth value) computed with \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAjAAAAAlCAYAAABcddNuAAAStklEQVR4Xu2dZ8t2RxHHkw+gsb2yESygICjGAqIBBbsERewhPKBo1BDQWGJDJPYWEDsKD2KsCUqIiQUiRBGsKCq+iIqvfGUlH0DnZ66BYd3dmd1T7nOuaw8Mz3Pf9zl7dv8zO/Pf2XIuvGBcA4GBwEBgIDAQGAgMBHaGwIU7q++o7kBgIDAQGAgMBAYCA4ELBoEZRjAQGAgMBAYCA4GBwO4QGARmOyp7iFTlTSKv206VRk0GAgOBgcBAIIPAW+R3N4r8eaBzdgisSWAeLc18scg7Zmruc6ScB4l8bqbyzrqYJ0sFfiSypk562zx02Yvcdp976aFqX9tYFd8n9fmGyG9mqtenpZyPBgPPMfiYufGbQw33lUKuE3mXyN9nKJDB3ytFPh4sbw69/kPedZnIj2eo/16LOPM4sFawpKEfEnlF0MCiCoUFXyxyDFmLvRCYocuode7nPsjLpRvsR5CNO0TmJFUEu6+LvCpIivbsY5bAb6pVQ15uEHlrEP/o+/Cf14s8Kxhjpur1P/Kep5wwgdlEHFiDwNDQm0SeGDSsqMHqfXTSf4rMldlpff9c9/cSGBzy/Z1K2FEC+rhH5f7aiGLoci5tb6ccyMu5g+Ov1YrA80in2n8wfdyzS3tvrlj69V9EPrwAVGrHz5CyI1MAU30M2D1d5Pkibw++c2qzo/itqVfe9V2RN4gskbnAlq8ReXwQvCl6PWUCs5k4sDSBwWB/KnK1yK1Bo+q57Y8rvKOnXi3PTCEwj5AXXSHykuSFL5OfCRQ2/Y7xPVOEjJi9PiM/MB1XStUPXbZocx/3Ygs/FHmciBfINdA9W+4lCNvr/fLDbSI2KEFgniBCkLi3ufl78v9PiNT8wWvk72RIooGoB+3WYNfjY7Qd4KvXYyp9rKcduWda8FtTr2TS/iSy5GCzlZT06BXMT5XAbCoOLE1gMCYcGWm9JS+C/80iDxeZY051ybqWyu4lMFqePq8/e+lNRkIQGS5S6roGolS/ocuzsIpl34nz/rxIa5YD560XUwG150nVK1kmU3ofp0n4C4KcZ79zIEMfuD3Y/ik+xva1pQnMFPyW1Cv+BR+ytI8mwN4pEl2f0qvXUyUwm4oDSxKYKR2pxzn9XB5C9roeZiqBwUF89QAcAeBhDogEr4ce7iFTU1tnMHTZY5HbfqY3oKgtaOuwoVr2Bof32sPNZPm8/rmWg6RKLOb8zqEfeBko7u/1MZbELU1gevFbWq+9ZLmnF7FwmWy05wO17B69niKB2VwcWJLA0JFIAS+ZBrbGrQH8fvLLPWZhphKYlkDR46yOQZc6Er5SbORYdq/1OHieIaCQeWtN569BlJ8r9Vpyytli1oJDr49Zi8Bov+7Bb0m99uLWa9utOPTU7xQJzOZi+lIEhjTe30S89HKvgeae03fuNThNJTAtGRXrrH7hkMxj0uUgMHf3HM089EzTTCHK3uCCkTPra5bySzm/wTvJEHlTWzzb62PWIjBT8FtSr2Q4GFQuvZTA6pd3kon2psZ79XpqBGaTcWApR6EBssdBTiE1Z9FRptTXPjuFwKQZFS9QWGfFAszaKPyYdLk0gUGHXHeJpIuha7s9WGj9QJF0d1hppw6Lb9OF2Twb3dmh+u/p/5YoeyP9FqIMbpSNrBnoWslcj4+JEhjsx+pQ7cnbsaV+ZAp+S+lVfdOag1nwaCVzrXo9NQKzyTjQ6sB0C67tUHSyv4rYOeReB4mxc9mycu8skYbe985FQqaUM4XAsOvgs4eXexkVbuMQJt0Z4gWhXky3qMslCAzE5I0ijOLtbhtGfy80RIP7OEqAHTi69ohFrZeLsFMPAvMFEXasoMOPifxARKdDwZOtuOzO4XkyBgTGa5P3Qki9A716Ax198dfGyD2izLoq3RnnEeUpgS4N/EoWc0TSVP9//219b09/KBEYtYnnST00U1DSq9dPW9thcVhSr72BD2zoE5ao69b8NN6kOuXn1ve26vUYCEzLkRqt+KhOFo0DEQKDIXHKIY7y+yK/EnmayC9FdDtlujCNQMEWSi8tS+B9sMglIrojRsvCKZ0XUWePU/cOKVJH0bNQzlNmrpPkfhcdBafPTiEwLYEidVaeDexRlyVdzU1g9FwLSIYezKW/062z6SJX3boM2YHA2F0Z1I/nUztPt+PyHDrnHBN2EV0kYgkUW5VrWQycb2TnWYrjFKLsZWPV/r0pYD0G4LFSOTAGX22Lkkm7zdtboE4bW/Do8TElAqOkRRffo9efiTCAu+UA/nsO7eTH2oLpKH65vrGkXqN4kQl7lAixhdhB/1BbIAgSQDVGgNNTRWqnM7fiEa2n4rdXAgMuV4mkR26kdpEuuN9kHPCClx5YQ8expEDnw2h0bmskyvWcKM9S/gNE2AnApbtndIcEOxY4/EnB9kYh2hE9Z5nrxBrccn+L/i6yTbRU1hQCYzMqdPrfVypsz/GI6GiPuiw1f24CoyQidaZ2Si+XEbMBTZ20jhhr5Js0txKjNKPBOxlgeDvL1M56UvqWKOPgvlKxM0bPGpi5zfM1ionXdzW7Yp0wJIVsFfrFh3zJ+JRoRhLiEJm66vEx3hSS9T0pgdMpLjCskbsofjmVLalXbZunf82unDc2jC0zNcpZRR88VFy35HsZPR2oRe28Va97IzD0G05AVhLoxbSU+G8yDtSMyo4Uc05VzwzIbY2MNhYQLRnC2H4nQppdT+61nd/bstnKuq0SmTMlEzTl+pc8HFk0lntHL4FJMyot9Y907j3qsoTBnARGcS9lMuyaglxQtmSE/qVOunamita/RJTVhmh/KXBPITCWKLfYWYQotwZgXeNAPfBj4MkUnO4uq/mntO7R0SXP9fiYKIEp6VXbUsuateJnMVhSr1ECo/XRfoHNMIDFjnWAYO177sxaq173RGD08xk6+IHkc7gsU9cIAx/vu1SbjAMlAmPJS85QLOnI/b2lsXaEQYblyyL2ZFAdHURGUlOcc4tDXuLeXgJjnWMkUNjDqrzRLu3cky694+uvP9iWnhxb0mNk0aQG0FJZ+i7ekRs5p8QT3XnfCvMIDO9S4pROT2lbe/uIDR5KGmr9wGYVIkS5NQBroCOo45CZctAzZiy2XtaWNrQE2R78tkxgltZrC7Y2rtBnWO/FWjA9o8pOdXnrr1p9V6tepxCYOZYrRHwUGKRT2vSX14vo2jptN4mIGonZZBwoERh1DiXSYElHzpBaGquBAIeLI7IGax1yxAm2GuESRKS3zF4C0xIorN6i01170qUNFL164LnIGirtI9gspKF2nTdO2N5nswje2g8baGu6szvMcu3o7SMtRNkGoiieLQTGlg/x48Aye2iZ3f3kTV2cOoFZWq8tBMb6J/TKWiB78KHadmSgtmUCM8dyhYiPAgPrY0oHnOqgp3bQ5CbjQK5z285fGr2oIZUITktjbao9BdCOpCLZgtaV51OC3NzP9hCY1kBhjTm6iHNPukT/5yqK0cWBHunAaXons2omK0I8SlVK15J5x6xHMjDeaL+XwNgpL6/NPUS5hcBYHwW26dSyZm2jgQ4fhETWwPT4GE8nnl6XnEJaWq8tBMaS71yw1amuyGC2dVdWq16nZGDmWK4Q8VHR+GDtr+SDNhkHcgRGCUWJrdkFiqWFVHQKLu8UXu/8Ek0ZRrMFLU4wDSpzpPUoc81dSK2BosVZKT571GWJMMy5BkaDireYsEZ0sddrRXT7tXfUvhfoeJf2AfpM7iON6tRa6h11hNrWHqKsthyZ8rGBLtcODXQe0dL6tjjnHh+zBoFpwU/bvYZe1RYiUz52MJvagR3MRrIPrUS9Va9TCMzcg99SeXbKrTZgtRmhkp42GQdSAmONpOTgrPMoZUV0BOSlby3AOWej5USzBa2HF1nFz5HWixKtnMH1ZGBaAkVKFiNOgHruUZdrEpjI2iywTzM62tfoQ3a9TC3TGCEwahO172ER4KO7bsCylSjbQBQlES27RpSg5Ppba6BrPWG0x8esQWBa8NP+sYZeo7t7rN5y/r51MNt6QGGrXvdAYGysLi16TqdjS1nITcaBlGBYQpEbCaULvkpsTcvxgqTdvldaS0Nni6w45z4cPArxMj+5ADdHWm/tXUgtGRWbdo987FEx2qMu1yAwlvDW7FwX0aVnu9ijzq3zRje6Ay9tR4TA6D21DItu//bOaerJqLR+Z8u2EWLCjghstXR5gywlC1EbV58Wyfz0+pg1CAx1i+BncZ0yAPJ2hOp7VF8ekfVij9q1l6XU9yrmkcxPj173QGAimZXIkhHw2WQcSAmM7Wi5FB5bPXEwnMuiI08AuEjEfhxPnZhHPGpzu3Z0QGf594GglMhJT2q84idX/1NrBqY1UFg2HnUCgHBMupxzCsl2/Np0De+023vBlH72ahEOotPMjA0mpTl+j8Corkr1UaPWukeDkM2oeH26lyhTN2wUTGpfEfbIgJJ6tXEcL1fp450tUxy9Psars6fXyBqYKH7Wsa2lV95D3Kh9ibyGQW7XKyT8AyKlw+yiUx7g0aPXPRAYL0FAu9lGjR/wYsIm40BKYCxpsCM4guvNIuzHv+nQYP7+W5H3iuRGjHaEaTuN/t9mc3JO0S4UZvSKgb9b5NZcYfI7rXvUKReKObNftxKY1kBhz3rwglAKwrHock4CA0Y2AwZp4LCtnxzAe5L8y/qWdKqmNCK1zoQiclkdO6LKZQzUYXmjXXXY3n3Uo5Uop4ei1YJWamfah2sZLcUgl2GxdQWfe4pcI1LLyKJDJFLPXh+zFoGJ4KeYr6nXyAcza+f2WF9HRuU6Efpb6Rtuat9RP9ej1z0QGItbrk+1LtHYXByoLeLF0MmycEEK9DAhNTQMiKBYSnd7ozw74syl+RRcfc9H5F2lURR15P57iUR2EqSOcws/txCYNNjVph1om82+8HO0Yysux6LLuQlMesZCakfpmQt6v37LKL3fBrpcFsWOUnmWUdNtIgTqK0TIjEZIidqEl+3QfmWPHa+RC+swtX4RYmBxqI3W7Ug8N0Vmp5fwXSyOLvkn3mnXIUUW3/f4mLSvpvrh73ce6kqdUnzt1IrXz3k+ku1YW6/e6D09CywdpKafOvC+Ms39ZGe8XX1qdz163QOBsb4fX8QnNsj4EmtYd4cfulyklBSw/ZL/by4O5AgMHYqP010iwpqOb4ugYL0wjheIfEvkRhE9ECdtLD/D2L4pkjtdVNec8E2lHJPGuXBsNHX4pEjNwWgH8dbc5Oq4ld9FCQxGxOcVIGv2yumKey8V0Q9q2fvBneAXcdzHosu5CYzimeJ8u/yBTEz6ZWGOv1e9cY/tFyW9Mp2kaXJLYNhhxDfK6KdclEd/9LZ/a52xCYL8ZQUbwB5fXrCdtO7cyycqtC7WzqjPHSLWh9i/p/8nmHGYZS74qE/gGYuLLUP9CnX8okjNP0HsWQcE9t7V42Mo91ymYDBhMMYx+dYm9FZ8K39XX2uLoJ/Xpk5q+FHOWelV9ZIbYFqccn8nJn1KhL5zXsSzJUicN+BVTHv0yrN7ITDUNfUt+q2tKHGx9repmO7tEvI6tfd3HeEsPa2DYy8RIa+OW/l7lMCcVX2PQZd0ZD4empKLs8K09b3eWonW8giQbxaprTlpLXOO+wlQZHdbszct79Zp8dxW81w5e/Ixa+DXgjX3aibqnQEC0lq2vZ8s5otEohs5evW6JwIzBc/02U3FgaUJjLI/bx56CsD6pd6owU5515LPbp3ADF0uqf1Y2XMTGN5KFqK2niBWs3nv0qm22pq3KW/UYMr3YCKj0L35mKXx68We4McaSrt4vbes3HOUz0aTKCmdotdTJTCbigNrEBgaDCu+WGTuERUGyw6PdIvqnJ1irbL2QGCGLteyhvx7liAwvIlyz4t4qfk1W68foON7OKWdJr31oZ3p1HiprL36mCXx68Wd55jigjh63/1qfYeStqi9TNXrKROYzcSBtQiMsjbWY8xFYjDAt4nYD1O1Gv2W7t8LgRm6PDurWYrA0CIyMS1rVdZAgaB0g0hpvUtPHViLwe7JCFnbu49ZAr8ezNNndC3TXCRG18jU1gbZOsyh11MnMJuIA2sSGBqModUW1bV0jtzppi3Pb+3ePRGYocuzsR57bkf0gK6Wms7ZP1ve6907Z71a/EbLvV4bzvLvc+I3VzvmrBNlcUVjyxx6HQTmbszn1GOzXtYmMHMZ/zGWk55ybNvIGoXolsBjxObU26Rz9czt64VNkEW4RSSyjuPUMRztHwj0IGDPz0qfj3xguOed45kgAoPABIFa6TZITO66S3459zqAlZo0XjMQGAgMBHaLANNNbHfPXdEjKHbb+K1XfBCYrWto1G8gMBAYCAwEBgIDgf9DYBCYYRQDgYHAQGAgMBAYCOwOgUFgdqeyUeGBwEBgIDAQGAgMBP4LF1UVj20LUicAAAAASUVORK5CYII=\" alt=\"a(n) = floor(H(n) + exp(H(n))ln(H(n)))-sigma(n)\" style=\"width: 280px; height: 18.5px;\" width=\"280\" height=\"18.5\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 21.0083px 8px; transform-origin: 21.0083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ewhere \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"H(n)\" style=\"width: 35.5px; height: 18.5px;\" width=\"35.5\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 20.6083px 8px; transform-origin: 20.6083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 7.775px 8px; transform-origin: 7.775px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eth \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/46000\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eharmonic number\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.5583px 8px; transform-origin: 15.5583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"sigma(n)\" style=\"width: 30.5px; height: 18.5px;\" width=\"30.5\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 20.6083px 8px; transform-origin: 20.6083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/46898\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003esum of divisors\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 9.71667px 8px; transform-origin: 9.71667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 28.7917px 8px; transform-origin: 28.7917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eLagarias \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://arxiv.org/abs/math/0008177\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003eproved\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.55px 8px; transform-origin: 15.55px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e that \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"a(n) \u003e= 0\" style=\"width: 56px; height: 18.5px;\" width=\"56\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 21px 8px; transform-origin: 21px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e for all \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 33.8333px 8px; transform-origin: 33.8333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e only if the \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://en.wikipedia.org/wiki/Riemann_hypothesis\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003eRiemann Hypothesis\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 24.8833px 8px; transform-origin: 24.8833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is true. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function a = LagariasRH(n)\r\n  a = floor(H(n)+exp(H(n))*ln(H(n))-sigma(n);\r\nend","test_suite":"%%\r\nn = 100;\r\ny = LagariasRH(n);\r\ny_correct = [0 0 1 0 4 0 7 2 7 5 13 0 17 9 12 8 23 5 27 8 21 20 34 1 33 25 30 17 46 7 50 22 40 37 46 6 62 43 50 19 70 19 74 37 46 55 82 9 79 46 70 47 95 32 83 38 81 74 107 2 112 81 76 56 102 45 125 70 103 58 133 14 138 101 94 81 129 60 151 48 116 115 160 23 142 122 137 80 173 33 158 105 148 136 163 34 192 122 140 82];\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 1000;\r\ny = LagariasRH(n);\r\nsum_correct = 914917;\r\nnprimes_correct = 155;\r\nassert(isequal(sum(y),sum_correct) \u0026\u0026 isequal(sum(isprime(y)),nprimes_correct))\r\n\r\n%%\r\nn = 10000;\r\ny = LagariasRH(n);\r\ny953_correct = [2461 4261 7113 8116 12978 11195 18980 16294 22215 21474];\r\nassert(isequal(y(953:953:n),y953_correct))\r\n\r\n%%\r\nn = 100000;\r\ny = LagariasRH(n);\r\nsum_correct = 13587430007;\r\nnprimes_correct = 8811;\r\nassert(isequal(sum(y),sum_correct) \u0026\u0026 isequal(sum(isprime(y)),nprimes_correct))\r\n\r\n%%\r\nn = 1000000;\r\ny = LagariasRH(n);\r\ny95395_correct = [308341 521204 855014 963930 1629129 1304492 2221964 1881773 2573303 2750908];\r\nassert(isequal(y(95395:95395:n),y95395_correct))\r\n\r\n%%\r\ny1 = LagariasRH(20403);\r\ny2 = LagariasRH(y1(end));\r\nf  = factor(y2(end));\r\ns3 = sum(LagariasRH(prod(f(end-2:end))));\r\ns3_correct = 350693690;\r\nassert(isequal(s3,s3_correct))\r\n\r\n%%\r\nfiletext = fileread('LagariasRH.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp') || contains(filetext, 'oeis') || contains(filetext, 'persistent'); \r\nassert(~illegal)","published":true,"deleted":false,"likes_count":2,"comments_count":2,"created_by":46909,"edited_by":46909,"edited_at":"2022-12-25T05:52:21.000Z","deleted_by":null,"deleted_at":null,"solvers_count":7,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2022-12-23T23:17:27.000Z","updated_at":"2026-02-03T17:06:47.000Z","published_at":"2022-12-23T23:19:21.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function that takes an input number \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and produces a sequence (i.e., all values up to and including the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003eth value) computed with \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle 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