A373485 a(n) = gcd(A083345(n), A276085(n)), where A276085 is fully additive with a(p) = p#/p, and A083345 is the numerator of the fully additive function with a(p) = 1/p.

0, 1, 1, 1, 1, 1, 1, 3, 2, 7, 1, 4, 1, 1, 8, 2, 1, 1, 1, 2, 2, 1, 1, 1, 2, 1, 1, 8, 1, 1, 1, 5, 2, 1, 12, 1, 1, 1, 8, 1, 1, 1, 1, 4, 1, 1, 1, 1, 2, 1, 4, 2, 1, 1, 8, 1, 2, 1, 1, 1, 1, 1, 17, 3, 6, 1, 1, 2, 2, 1, 1, 1, 1, 1, 1, 4, 6, 1, 1, 1, 4, 1, 1, 1, 2, 1, 8, 1, 1, 1, 20, 4, 2, 1, 12, 1, 1, 1, 1, 7, 1, 1, 1, 1, 1

Offset: 1

Author

Antti Karttunen, Jun 09 2024

Keywords

• nonn

Comments

For all n >= 1, A373145(n) is a multiple of a(n).

For all i, j: A373151(i) = A373151(j) => a(i) = a(j) => A373483(i) = A373483(j).

Links

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

Crossrefs

Cf. A083345, A276085, A373145, A373151.

Cf. A369002 (positions of even terms), A369003 (of odd terms), A373483, A373484 (of multiples of 3).

Programs

PARI

A083345(n) = { my(f=factor(n)); numerator(vecsum(vector(#f~, i, f[i, 2]/f[i, 1]))); };
A276085(n) = { my(f = factor(n)); sum(k=1, #f~, f[k, 2]*prod(i=1,primepi(f[k, 1]-1),prime(i))); };
A373485(n) = gcd(A083345(n), A276085(n));