A294810 a(n) = Sum_{d|n} d^(n+2).

1, 17, 244, 4161, 78126, 1686434, 40353608, 1074791425, 31381236757, 1000244144722, 34522712143932, 1283997101947770, 51185893014090758, 2177986570740006274, 98526126098761952664, 4722384497336874434561, 239072435685151324847154

Offset

1,2

Links

Seiichi Manyama, Table of n, a(n) for n = 1..384

Formula

G.f.: Sum_{k>0} k^(k+2)*x^k/(1-(k*x)^k).

L.g.f.: -log(Product_{k>=1} (1 - (k*x)^k)^k) = Sum_{k>=1} a(k)*x^k/k. - Seiichi Manyama, Jun 02 2019

Mathematica

Table[Total[Divisors[n]^(n+2)], {n, 20}] (* Harvey P. Dale, Dec 23 2023 *)

Prog

(PARI) {a(n) = sigma(n, n+2)}
(PARI) N=66; x='x+O('x^N); Vec(sum(k=1, N, k^(k+2)*x^k/(1-(k*x)^k)))
(PARI) N=20; x='x+O('x^N); Vec(x*deriv(-log(prod(k=1, N, (1-(k*x)^k)^k)))) \\ Seiichi Manyama, Jun 02 2019

Crossrefs

Cf. A294645, A294809.

Sequence in context: A259347 A324358 A294608 * A362233 A214175 A309856

Adjacent sequences: A294807 A294808 A294809 * A294811 A294812 A294813

Keyword

nonn

Author

Seiichi Manyama, Nov 09 2017

Status

approved