A373835 a(n) = gcd(bigomega(n), A276085(n)), where bigomega (A001222), and A276085 are fully additive with a(p) = 1 and a(p) = p#/p respectively.

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

Offset: 1

Author

Antti Karttunen, Jun 19 2024

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..100000

Crossrefs

Cf. A001222, A276085, A373833 [= a(A276086(n))], A373836, A373837 (positions of multiples of 3).

Programs

PARI

A276085(n) = { my(f = factor(n)); sum(k=1, #f~, f[k, 2]*prod(i=1,primepi(f[k, 1]-1),prime(i))); };
A373835(n) = gcd(bigomega(n), A276085(n));