A283535 a(n) = Sum_{d|n} d^(3*d + 1).

1, 129, 59050, 67108993, 152587890626, 609359740069674, 3909821048582988050, 37778931862957228818561, 523347633027360537213570571, 10000000000000000000152587890754, 255476698618765889551019445759400442, 8505622499821102144576132293474637113130

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))) = Sum_{k>=1} a(k)*x^k/k. - Seiichi Manyama, Jun 18 2019

Example

a(6) = 1^(3+1) + 2^(6+1) + 3^(9+1) + 6^(18+1) = 609359740069674.

Mathematica

f[n_] := Block[{d = Divisors[n]}, Total[d^(3 d + 1)]]; Array[f, 12] (* Robert G. Wilson v, Mar 10 2017 *)

Prog

(PARI) a(n) = sumdiv(n, d, d^(3*d+1)); \\ Michel Marcus, Mar 11 2017
(PARI) N=20; x='x+O('x^N); Vec(x*deriv(-log(prod(k=1, N, (1-x^k)^k^(3*k))))) \\ Seiichi Manyama, Jun 18 2019

Crossrefs

Cf. Sum_{d|n} d^(k*d+1): A283498 (k=1), A283533 (k=2), this sequence (k=3).

Cf. A308697.

Sequence in context: A196752 A143006 A176368 * A183553 A242229 A351137

Adjacent sequences: A283532 A283533 A283534 * A283536 A283537 A283538

Keyword

nonn

Author

Seiichi Manyama, Mar 10 2017

Status

approved