A341833 - OEIS

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

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OFFSET

1,2

COMMENTS

Dirichlet inverse of A111217.

LINKS

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

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).

MATHEMATICA

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