A374112 a(n) = gcd(A113177(n), A276085(n)), where A113177 and A276085 are fully additive with a(p) = Fibonacci(p) and a(p) = p#/p, respectively.

0, 1, 2, 2, 1, 3, 1, 3, 4, 1, 1, 4, 1, 1, 1, 4, 1, 5, 1, 1, 1, 1, 1, 5, 2, 1, 6, 1, 1, 1, 1, 5, 1, 1, 18, 6, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 6, 2, 1, 1, 1, 1, 7, 2, 1, 1, 1, 1, 1, 1, 1, 17, 6, 2, 1, 1, 1, 1, 1, 1, 7, 1, 1, 2, 1, 6, 1, 1, 1, 8, 1, 1, 17, 6, 1, 1, 1, 1, 1, 6, 1, 1, 1, 2, 7, 1, 1, 1, 2, 1, 1, 1, 1, 2

Offset: 1

Author

Antti Karttunen, Jun 29 2024

Keywords

• nonn

Links

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

Crossrefs

Cf. A113177, A276085, A374113, A374114 (indices of even terms), A374115 (of odd terms).

Cf. also A374116.

Programs

PARI

A113177(n) = if(n<=1, 0, my(f=factor(n)); sum(i=1, #f~, f[i, 2]*fibonacci(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))); };
A374112(n) = gcd(A113177(n), A276085(n));