A341832 Dirichlet g.f.: 1 / zeta(s)^6.

1, -6, -6, 15, -6, 36, -6, -20, 15, 36, -6, -90, -6, 36, 36, 15, -6, -90, -6, -90, 36, 36, -6, 120, 15, 36, -20, -90, -6, -216, -6, -6, 36, 36, 36, 225, -6, 36, 36, 120, -6, -216, -6, -90, -90, 36, -6, -90, 15, -90, 36, -90, -6, 120, 36, 120, 36, 36, -6, 540, -6, 36, -90, 1, 36

Offset: 1

Author

Ilya Gutkovskiy, Feb 21 2021

Keywords

• sign
• mult

Comments

Dirichlet inverse of A034695.

Links

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

Crossrefs

Row 6 of A346148.

Cf. A007427, A007428, A008683, A034695, A247343, A341831, A341833, A341834, A341835, A341836.

Programs

Mathematica

a[1] = 1; a[n_] := Times @@ ((-1)^#[[2]] Binomial[6, #[[2]]] &/@ FactorInteger[n]); Table[a[n], {n, 65}]

PARI

for(n=1, 100, print1(direuler(p=2, n, (1 - X)^6)[n], ", ")) \\ Vaclav Kotesovec, Feb 22 2021

Formula

Multiplicative with a(p^e) = (-1)^e * binomial(6, e).

a(1) = 1; a(n) = -Sum_{d|n, d < n} tau_6(n/d) * a(d).