A308689 a(n) = Sum_{d|n} d^(3*n/d - 2).

1, 3, 4, 21, 6, 216, 8, 1289, 2197, 8828, 12, 142278, 14, 526704, 1672464, 5246993, 18, 76887669, 20, 345319966, 1163085032, 2147498312, 24, 52918480178, 1220703151, 137438982060, 847293392440, 1374672048414, 30, 31838544112466, 32, 87962004029473

Offset: 1

Author

Seiichi Manyama, Jun 17 2019

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..1000

Crossrefs

Column k=3 of A308690.

Cf. A308692, A308693.

Programs

Mathematica

a[n_] := DivisorSum[n, #^(3*n/# - 2) &]; Array[a, 32] (* Amiram Eldar, May 09 2021 *)

PARI

{a(n) = sumdiv(n, d, d^(3*n/d-2))}

PARI

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

Formula

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

a(p) = p+1 for prime p.

G.f.: Sum_{k>=1} k*x^k/(1 - k^3*x^k). - Ilya Gutkovskiy, Jul 25 2019