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A321222
a(n) = Sum_{d|n} mu(d)*d^n.
7
1, -3, -26, -15, -3124, 45864, -823542, -255, -19682, 9990233352, -285311670610, 2176246800, -302875106592252, 11111328602468784, 437893859848932344, -65535, -827240261886336764176, 101559568985784, -1978419655660313589123978, 99999904632567310800
OFFSET
1,2
LINKS
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).
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}]
PROG
(PARI) a(n) = sumdiv(n, d, moebius(d)*d^n) \\ Andrew Howroyd, Nov 06 2018
KEYWORD
sign
AUTHOR
Ilya Gutkovskiy, Nov 06 2018
STATUS
approved