A283533 a(n) = Sum_{d|n} d^(2*d + 1).

1, 33, 2188, 262177, 48828126, 13060696236, 4747561509944, 2251799813947425, 1350851717672994277, 1000000000000048828158, 895430243255237372246532, 953962166440690142662256812, 1192533292512492016559195008118

Offset

1,2

Comments

Inverse Mobius transform of A085526. - R. J. Mathar, Mar 11 2017

Links

Seiichi Manyama, Table of n, a(n) for n = 1..214

Formula

L.g.f.: -log(Product_{k>=1} (1 - x^k)^(k^(2*k))) = Sum_{k>=1} a(k)*x^k/k. - Seiichi Manyama, Jun 18 2019

Example

a(6) = 1^(2+1) + 2^(4+1) + 3^(6+1) + 6^(12+1) = 13060696236.

Mathematica

f[n_] := Block[{d = Divisors[n]}, Total[d^(2 d + 1)]]; Array[f, 14] (* Robert G. Wilson v, Mar 10 2017 *)

Prog

(PARI) a(n) = sumdiv(n, d, d^(2*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^(2*k))))) \\ Seiichi Manyama, Jun 18 2019

Crossrefs

Cf. Sum_{d|n} d^(k*d+1): A283498 (k=1), this sequence (k=2), A283535 (k=3).

Cf. A308696.

Sequence in context: A284112 A099370 A267672 * A294773 A294611 A294954

Adjacent sequences: A283530 A283531 A283532 * A283534 A283535 A283536

Keyword

nonn

Author

Seiichi Manyama, Mar 10 2017

Status

approved