A054610 - OEIS

%I #25 May 07 2021 06:57:56

%S 0,3,12,33,96,255,780,2205,6672,19755,59340,177177,532416,1594359,

%T 4785228,14349525,43053504,129140211,387441756,1162261521,3486844320,

%U 10460357775,31381236876,94143178893,282430082832,847288610475

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

%C Dirichlet convolution of phi(n) and 3^n. - _Richard L. Ollerton_, May 07 2021

%H Seiichi Manyama, <a href="/A054610/b054610.txt">Table of n, a(n) for n = 0..2095</a>

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

%F a(n) = 3*A034754(n). - _R. J. Mathar_, May 18 2014

%F a(n) = Sum_{k=1..n} 3^gcd(n,k). - _Ilya Gutkovskiy_, Apr 16 2021

%F 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

%o (PARI) a(n) = sum(k=1, n, 3^gcd(n,k)); \\ _Michel Marcus_, Apr 16 2021

%Y Column k=3 of A185651.

%Y Cf. A001867, A034754.

%K nonn

%O 0,2

%A _N. J. A. Sloane_, Apr 16 2000