Problem 52804. Easy Sequences 29: Odd proper divisors of odd proper divisors

Ramon Villamangca

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The number  is special. It has odd number of proper divisors:  . Furthermore, if you take any of its proper divisors, say , it too has odd number of proper divisors: . The numbers  and , have similar property as . 
Given a limit n, find how many integers , have similar property as 210, namely, the integers should have odd number of proper divisors and all its proper divisors have odd number of proper divisors, as well. 
The number , does not qualify because it has even proper divisors, 8 in total  . The number  also doesn't qualify because although it has proper divisors, some of its divisor, like , have even number of proper divisors. 
NOTE: A proper divisor of a number, is a divisor which is less than the number. Exception to this rule is the number 1, which is considered a proper divisor of itself.