A308693 - OEIS

%I #21 May 09 2021 02:51:00

%S 1,2,2,10,2,93,2,578,731,4223,2,56765,2,262489,547068,2359810,2,

%T 31173510,2,152949071,387538140,1073743157,2,20134371189,244140627,

%U 68719478935,282430067924,618515646977,2,12056339359929,2,39582552821762,205891133866212

%N a(n) = Sum_{d|n} d^(3*(n/d - 1)).

%F L.g.f.: -log(Product_{k>=1} (1 - k^3*x^k)^(1/k^4)) = Sum_{k>=1} a(k)*x^k/k.

%F a(p) = 2 for prime p.

%F G.f.: Sum_{k>=1} x^k/(1 - k^3*x^k). - _Ilya Gutkovskiy_, Jul 25 2019

%t a[n_] := DivisorSum[n, #^(3*(n/# - 1)) &]; Array[a, 33] (* _Amiram Eldar_, May 09 2021 *)

%o (PARI) {a(n) = sumdiv(n, d, d^(3*(n/d-1)))}

%o (PARI) N=66; x='x+O('x^N); Vec(x*deriv(-log(prod(k=1, N, (1-k^3*x^k)^(1/k^4)))))

%Y Column k=3 of A308694.

%K nonn

%O 1,2

%A _Seiichi Manyama_, Jun 17 2019