A359700 a(n) = Sum_{d|n} d^(d + n/d - 1).

1, 5, 28, 265, 3126, 46754, 823544, 16778273, 387420733, 10000015690, 285311670612, 8916100733146, 302875106592254, 11112006831323074, 437893890380939688, 18446744073843786241, 827240261886336764178, 39346408075300026047027

Offset

1,2

Links

Seiichi Manyama, Table of n, a(n) for n = 1..386

Formula

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

If p is prime, a(p) = 1 + p^p.

Mathematica

a[n_] := DivisorSum[n, #^(# + n/# - 1) &]; Array[a, 20] (* Amiram Eldar, Aug 14 2023 *)

Prog

(PARI) a(n) = sumdiv(n, d, d^(d+n/d-1));
(PARI) my(N=20, x='x+O('x^N)); Vec(sum(k=1, N, (k*x)^k/(1-k*x^k)))

Crossrefs

Cf. A014566, A055225, A087909, A294956, A353013, A353014.

Sequence in context: A347399 A353009 A343573 * A342677 A224607 A320974

Adjacent sequences: A359697 A359698 A359699 * A359701 A359702 A359703

Keyword

nonn

Author

Seiichi Manyama, Jan 11 2023

Status

approved