A345059 a(n) = A129283(n) / gcd(sigma(n), A129283(n)), where A129283(n) is the sum of n and its arithmetic derivative.

1, 1, 1, 8, 1, 11, 1, 4, 15, 17, 1, 1, 1, 23, 23, 48, 1, 1, 1, 22, 31, 35, 1, 17, 35, 41, 27, 15, 1, 61, 1, 16, 47, 53, 47, 96, 1, 59, 55, 6, 1, 83, 1, 23, 14, 71, 1, 40, 21, 95, 71, 54, 1, 9, 71, 37, 79, 89, 1, 19, 1, 95, 57, 256, 83, 127, 1, 10, 95, 43, 1, 76, 1, 113, 65, 39, 95, 149, 1, 128, 189, 125, 1, 13, 107

Offset: 1

Author

Antti Karttunen, Jun 07 2021

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..12800
• Antti Karttunen, Data supplement: n, a(n) computed for n = 1..65537
• Index entries for sequences related to sigma(n)

Crossrefs

Cf. A000203, A003415, A129283, A211991, A343226, A343227.

Programs

PARI

A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A129283(n) = (n+A003415(n));
A345059(n) = { my(u=A129283(n)); (u/gcd(u,sigma(n))); };

Formula

a(n) = A129283(n) / A343226(n) = A129283(n) / gcd(A000203, A129283(n)).