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A321385
a(n) = Sum_{d|n} (-1)^(n/d+1)*d^d.
4
1, 3, 28, 251, 3126, 46632, 823544, 16776955, 387420517, 9999996878, 285311670612, 8916100401824, 302875106592254, 11112006824734476, 437893890380862528, 18446744073692774139, 827240261886336764178, 39346408075296150201567, 1978419655660313589123980, 104857599999999989999997126
OFFSET
1,2
LINKS
FORMULA
G.f.: Sum_{k>=1} k^k*x^k/(1 + x^k).
a(n) ~ n^n. - Vaclav Kotesovec, Nov 09 2018
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]]
PROG
(PARI) a(n) = sumdiv(n, d, (-1)^(n/d+1)*d^d); \\ Michel Marcus, Nov 09 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Nov 08 2018
STATUS
approved