A321385 a(n) = Sum_{d|n} (-1)^(n/d+1)*d^d.

1, 3, 28, 251, 3126, 46632, 823544, 16776955, 387420517, 9999996878, 285311670612, 8916100401824, 302875106592254, 11112006824734476, 437893890380862528, 18446744073692774139, 827240261886336764178, 39346408075296150201567, 1978419655660313589123980, 104857599999999989999997126

Offset: 1

Author

Ilya Gutkovskiy, Nov 08 2018

Keywords

• nonn

Links

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

Crossrefs

Cf. A000312, A062796, A321387.

Programs

Mathematica

Table[Sum[(-1)^(n/d + 1) d^d, {d, Divisors[n]}], {n, 20}]
nmax = 20; Rest[CoefficientList[Series[Sum[k^k x^k/(1 + x^k), {k, 1, nmax}], {x, 0, nmax}], x]]

PARI

a(n) = sumdiv(n, d, (-1)^(n/d+1)*d^d); \\ Michel Marcus, Nov 09 2018

Formula

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

a(n) ~ n^n. - Vaclav Kotesovec, Nov 09 2018