A321222 a(n) = Sum_{d|n} mu(d)*d^n.

1, -3, -26, -15, -3124, 45864, -823542, -255, -19682, 9990233352, -285311670610, 2176246800, -302875106592252, 11111328602468784, 437893859848932344, -65535, -827240261886336764176, 101559568985784, -1978419655660313589123978, 99999904632567310800

Offset: 1

Author

Ilya Gutkovskiy, Nov 06 2018

Keywords

• sign

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..388

Crossrefs

Cf. A008683, A023900, A046970, A063453, A067858, A189922, A189923.

Programs

Mathematica

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

PARI

a(n) = sumdiv(n, d, moebius(d)*d^n) \\ Andrew Howroyd, Nov 06 2018

Formula

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

a(n) = Product_{p|n, p prime} (1 - p^n).