A341836 Dirichlet g.f.: 1 / zeta(s)^10.

1, -10, -10, 45, -10, 100, -10, -120, 45, 100, -10, -450, -10, 100, 100, 210, -10, -450, -10, -450, 100, 100, -10, 1200, 45, 100, -120, -450, -10, -1000, -10, -252, 100, 100, 100, 2025, -10, 100, 100, 1200, -10, -1000, -10, -450, -450, 100, -10, -2100, 45, -450, 100, -450

Offset: 1

Author

Ilya Gutkovskiy, Feb 21 2021

Keywords

• sign
• mult

Comments

Dirichlet inverse of A111220.

Links

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

Crossrefs

Row 10 of A346148.

Cf. A007427, A007428, A008683, A111220, A247343, A341831, A341832, A341833, A341834, A341835.

Programs

Mathematica

a[1] = 1; a[n_] := Times @@ ((-1)^#[[2]] Binomial[10, #[[2]]] &/@ FactorInteger[n]); Table[a[n], {n, 52}]

PARI

for(n=1, 100, print1(direuler(p=2, n, (1 - X)^10)[n], ", ")) \\ Vaclav Kotesovec, Feb 22 2021

Formula

Multiplicative with a(p^e) = (-1)^e * binomial(10, e).

a(1) = 1; a(n) = -Sum_{d|n, d < n} tau_10(n/d) * a(d).