A308697 a(n) = Sum_{d|n} d^(3*d).

1, 65, 19684, 16777281, 30517578126, 101559956688164, 558545864083284008, 4722366482869661990977, 58149737003040059690409853, 1000000000000000000030517578190, 23225154419887808141001767796309132, 708801874985091845381344408569542626596

Offset

1,2

Links

Seiichi Manyama, Table of n, a(n) for n = 1..152

Formula

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

G.f.: Sum_{k>=1} k^(3*k) * x^k/(1 - x^k).

Mathematica

a[n_] := DivisorSum[n, #^(3*#) &]; Array[a, 12] (* Amiram Eldar, May 09 2021 *)

Prog

(PARI) {a(n) = sumdiv(n, d, d^(3*d))}
(PARI) N=20; x='x+O('x^N); Vec(x*deriv(-log(prod(k=1, N, (1-x^k)^k^(3*k-1)))))
(PARI) N=20; x='x+O('x^N); Vec(sum(k=1, N, k^(3*k)*x^k/(1-x^k)))

Crossrefs

Column k=3 of A308698.

Cf. A073706, A308757.

Sequence in context: A264541 A323316 A120801 * A368890 A283580 A355496

Adjacent sequences: A308694 A308695 A308696 * A308698 A308699 A308700

Keyword

nonn

Author

Seiichi Manyama, Jun 17 2019

Status

approved