A341834 Dirichlet g.f.: 1 / zeta(s)^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

Author

Ilya Gutkovskiy, Feb 21 2021

Keywords

• sign
• mult

Comments

Dirichlet inverse of A111218.

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..10000

Crossrefs

Row 8 of A346148.

Cf. A007427, A007428, A008683, A111218, A247343, A341831, A341832, A341833, A341835, A341836.

Programs

Mathematica

a[1] = 1; a[n_] := Times @@ ((-1)^#[[2]] Binomial[8, #[[2]]] &/@ FactorInteger[n]); Table[a[n], {n, 60}]

PARI

for(n=1, 100, print1(direuler(p=2, n, (1 - X)^8)[n], ", ")) \\ Vaclav Kotesovec, Feb 22 2021

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).