A054610 a(n) = Sum_{d|n} phi(d)*3^(n/d).

0, 3, 12, 33, 96, 255, 780, 2205, 6672, 19755, 59340, 177177, 532416, 1594359, 4785228, 14349525, 43053504, 129140211, 387441756, 1162261521, 3486844320, 10460357775, 31381236876, 94143178893, 282430082832, 847288610475

Offset: 0

Author

N. J. A. Sloane, Apr 16 2000

Keywords

• nonn

Comments

Dirichlet convolution of phi(n) and 3^n. - Richard L. Ollerton, May 07 2021

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..2095

Crossrefs

Column k=3 of A185651.

Cf. A001867, A034754.

Programs

PARI

a(n) = sum(k=1, n, 3^gcd(n,k)); \\ Michel Marcus, Apr 16 2021

Formula

a(n) = n * A001867(n).

a(n) = 3*A034754(n). - R. J. Mathar, May 18 2014

a(n) = Sum_{k=1..n} 3^gcd(n,k). - Ilya Gutkovskiy, Apr 16 2021

a(n) = Sum_{k=1..n} 3^(n/gcd(n,k))*phi(gcd(n,k))/phi(n/gcd(n,k)). - Richard L. Ollerton, May 07 2021