A373369 a(n) = gcd(A001414(n), A059975(n)), where A001414 and A059975 are fully additive with a(p) = p and a(p) = p-1, respectively.

0, 1, 1, 2, 1, 1, 1, 3, 2, 1, 1, 1, 1, 1, 2, 4, 1, 1, 1, 3, 2, 1, 1, 1, 2, 1, 3, 1, 1, 1, 1, 5, 2, 1, 2, 2, 1, 1, 2, 1, 1, 3, 1, 3, 1, 1, 1, 1, 2, 3, 2, 1, 1, 1, 2, 1, 2, 1, 1, 4, 1, 1, 1, 6, 2, 1, 1, 3, 2, 1, 1, 1, 1, 1, 1, 1, 2, 3, 1, 1, 4, 1, 1, 2, 2, 1, 2, 1, 1, 1, 2, 3, 2, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 3

Offset: 1

Author

Antti Karttunen, Jun 05 2024

Keywords

• nonn

Links

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

Crossrefs

Cf. A001414, A059975, A345452 (positions of even terms).

Cf. also A082299, A306709, A373362, A373363, A373364, A373365.

Programs

PARI

A001414(n) = ((n=factor(n))[, 1]~*n[, 2]);
A059975(n) = {my(f = factor(n)); sum(i = 1, #f~, f[i, 2]*(f[i, 1] - 1)); };
A373369(n) = gcd(A001414(n), A059975(n));