Could not figure out how to speed up my code. Ended up having to use a lookup table to speed it up sufficiently.
There is a shortcut using Mobius Inversion...
I too had problems with the time limit for large arguments and had to resort to a few tricks. But my solution is still general.
Word Counting and Indexing
vectorization in N
Back to basics 23 - Triangular matrix
Center of mass
Easy Sequences 7: Easy as Composite Pi
Easy Sequences 23: Hat Guessing Game!
Easy Sequences 38: Prime Number Delta
Easy Sequences 26: Prime-Integer Line Segments
Easy Sequences 14: Consecutive Composites
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