A308757 a(n) = Sum_{d|n} d^(3*(d-2)).

1, 2, 28, 4098, 1953126, 2176782365, 4747561509944, 18014398509486082, 109418989131512359237, 1000000000000000001953127, 13109994191499930367061460372, 237376313799769806328952468217885, 5756130429098929077956071497934208654

Offset

1,2

Links

Seiichi Manyama, Table of n, a(n) for n = 1..154

Formula

L.g.f.: -log(Product_{k>=1} (1 - x^k)^(k^(3*k-7))) = Sum_{k>=1} a(k)*x^k/k.

G.f.: Sum_{k>=1} k^(3*(k-2)) * x^k/(1 - x^k).

Mathematica

a[n_] := DivisorSum[n, #^(3*(# - 2)) &]; Array[a, 13] (* Amiram Eldar, May 08 2021 *)

Prog

(PARI) {a(n) = sumdiv(n, d, d^(3*(d-2)))}
(PARI) N=20; x='x+O('x^N); Vec(x*deriv(-log(prod(k=1, N, (1-x^k)^k^(3*k-7)))))
(PARI) N=20; x='x+O('x^N); Vec(sum(k=1, N, k^(3*(k-2))*x^k/(1-x^k)))

Crossrefs

Cf. A283535, A308697.

Sequence in context: A085602 A058502 A080266 * A180423 A090497 A128371

Adjacent sequences: A308754 A308755 A308756 * A308758 A308759 A308760

Keyword

nonn

Author

Seiichi Manyama, Jun 22 2019

Status

approved