A373976 a(n) = A001222(n) - A001222(A001414(n)), where A001222 is bigomega, the number of prime factors with multiplicity, and A001414 is sopfr, sum of prime factors with multiplicity. a(1) = 0 by convention.

0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 2, 0, 0, -1, 1, 0, 0, 0, 1, 0, 1, 0, 2, 0, 0, 1, 2, 0, 1, 0, 3, 0, 1, -1, 2, 0, 0, -2, 3, 0, 0, 0, 1, 2, 0, 0, 4, 0, 0, -1, 2, 0, 3, -2, 3, 0, 1, 0, 1, 0, 0, 2, 3, -1, -1, 0, 1, 0, 1, 0, 2, 0, 0, 2, 2, -1, 0, 0, 4, 1, 1, 0, 2, 0, -1, -3, 3, 0, 3, -1, 0, 0, 0, -2, 5, 0, -1, 2, 2, 0

Offset: 1

Author

Antti Karttunen, Jun 24 2024

Keywords

• sign

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537

Crossrefs

Cf. A001222, A001414, A342956.

Cf. also A045835.

Programs

PARI

A001414(n) = ((n=factor(n))[, 1]~*n[, 2]); \\ From A001414.
A373976(n) = if(1==n, 0, bigomega(n)-bigomega(A001414(n)));

Formula

a(n) = A001222(n) - A342956(n).