A341833 Dirichlet g.f.: 1 / zeta(s)^7.

1, -7, -7, 21, -7, 49, -7, -35, 21, 49, -7, -147, -7, 49, 49, 35, -7, -147, -7, -147, 49, 49, -7, 245, 21, 49, -35, -147, -7, -343, -7, -21, 49, 49, 49, 441, -7, 49, 49, 245, -7, -343, -7, -147, -147, 49, -7, -245, 21, -147, 49, -147, -7, 245, 49, 245, 49, 49, -7, 1029, -7, 49

Offset: 1

Author

Ilya Gutkovskiy, Feb 21 2021

Keywords

• sign
• mult

Comments

Dirichlet inverse of A111217.

Links

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

Crossrefs

Row 7 of A346148.

Cf. A007427, A007428, A008683, A111217, A247343, A341831, A341832, A341834, A341835, A341836.

Programs

Mathematica

a[1] = 1; a[n_] := Times @@ ((-1)^#[[2]] Binomial[7, #[[2]]] &/@ FactorInteger[n]); Table[a[n], {n, 62}]

PARI

for(n=1, 100, print1(direuler(p=2, n, (1 - X)^7)[n], ", ")) \\ Vaclav Kotesovec, Feb 22 2021

Formula

Multiplicative with a(p^e) = (-1)^e * binomial(7, e).

a(1) = 1; a(n) = -Sum_{d|n, d < n} tau_7(n/d) * a(d).