A308763 - OEIS

%I #23 May 08 2021 06:26:33

%S 1,2,4,21,126,1394,16808,266305,4785157,100390882,2357947692,

%T 61978939050,1792160394038,56707753666594,1946196290656824,

%U 72061992352890881,2862423051509815794,121441386937936123331,5480386857784802185940,262145000003883417004506

%N a(n) = Sum_{d|n} d^(n-2).

%H Seiichi Manyama, <a href="/A308763/b308763.txt">Table of n, a(n) for n = 1..388</a>

%F L.g.f.: -log(Product_{k>=1} (1 - (k*x)^k)^(1/k^3)) = Sum_{k>=1} a(k)*x^k/k.

%F G.f.: Sum_{k>=1} k^(k-2) * x^k/(1 - (k*x)^k).

%t a[n_] := DivisorSum[n, #^(n - 2) &]; Array[a, 20] (* _Amiram Eldar_, May 08 2021 *)

%o (PARI) {a(n) = sigma(n, n-2)}

%o (PARI) N=20; x='x+O('x^N); Vec(x*deriv(-log(prod(k=1, N, (1-(k*x)^k)^(1/k^3)))))

%o (PARI) N=20; x='x+O('x^N); Vec(sum(k=1, N, k^(k-2)*x^k/(1-(k*x)^k)))

%Y Cf. A023887, A082245, A294645, A294810, A308755.

%K nonn

%O 1,2

%A _Seiichi Manyama_, Jun 23 2019