A294956 a(n) = Sum_{d|n} d^(d + n/d).

1, 9, 82, 1041, 15626, 280212, 5764802, 134221889, 3486785131, 100000078254, 3138428376722, 106993207077516, 3937376385699290, 155568095598166344, 6568408355713287812, 295147905180426634241, 14063084452067724991010

Offset: 1

Author

Seiichi Manyama, Nov 12 2017

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..385

Crossrefs

Cf. A055225, A062796, A294957.

Programs

Mathematica

sd[n_]:=Total[#^(#+n/#)&/@Divisors[n]]; Array[sd,20] (* Harvey P. Dale, Mar 28 2021 *)

PARI

a(n) = sumdiv(n, d, d^(d+n/d));

PARI

N=20; x='x+O('x^N); Vec(x*deriv(-log(prod(k=1, N, (1-k*x^k)^(k^(k-1)))))) \\ Seiichi Manyama, Jun 09 2019

PARI

my(N=20, x='x+O('x^N)); Vec(sum(k=1, N, k^(k+1)*x^k/(1-k*x^k))) \\ Seiichi Manyama, Jan 11 2023

Formula

L.g.f.: -log(Product_{k>=1} (1 - k*x^k)^(k^(k-1))) = Sum_{k>=1} a(k)*x^k/k. - Seiichi Manyama, Jun 09 2019

G.f.: Sum_{k>0} k^(k+1) * x^k / (1 - k * x^k). - Seiichi Manyama, Jan 11 2023