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A341834
Dirichlet g.f.: 1 / zeta(s)^8.
8
1, -8, -8, 28, -8, 64, -8, -56, 28, 64, -8, -224, -8, 64, 64, 70, -8, -224, -8, -224, 64, 64, -8, 448, 28, 64, -56, -224, -8, -512, -8, -56, 64, 64, 64, 784, -8, 64, 64, 448, -8, -512, -8, -224, -224, 64, -8, -560, 28, -224, 64, -224, -8, 448, 64, 448, 64, 64, -8, 1792
OFFSET
1,2
COMMENTS
Dirichlet inverse of A111218.
LINKS
FORMULA
Multiplicative with a(p^e) = (-1)^e * binomial(8, e).
a(1) = 1; a(n) = -Sum_{d|n, d < n} tau_8(n/d) * a(d).
MATHEMATICA
a[1] = 1; a[n_] := Times @@ ((-1)^#[[2]] Binomial[8, #[[2]]] &/@ FactorInteger[n]); Table[a[n], {n, 60}]
PROG
(PARI) for(n=1, 100, print1(direuler(p=2, n, (1 - X)^8)[n], ", ")) \\ Vaclav Kotesovec, Feb 22 2021
KEYWORD
sign,mult
AUTHOR
Ilya Gutkovskiy, Feb 21 2021
STATUS
approved