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A341831
Dirichlet g.f.: 1 / zeta(s)^5.
8
1, -5, -5, 10, -5, 25, -5, -10, 10, 25, -5, -50, -5, 25, 25, 5, -5, -50, -5, -50, 25, 25, -5, 50, 10, 25, -10, -50, -5, -125, -5, -1, 25, 25, 25, 100, -5, 25, 25, 50, -5, -125, -5, -50, -50, 25, -5, -25, 10, -50, 25, -50, -5, 50, 25, 50, 25, 25, -5, 250, -5, 25, -50, 0, 25
OFFSET
1,2
COMMENTS
Dirichlet inverse of A061200.
LINKS
FORMULA
Multiplicative with a(p^e) = (-1)^e * binomial(5, e).
a(1) = 1; a(n) = -Sum_{d|n, d < n} tau_5(n/d) * a(d).
MATHEMATICA
a[1] = 1; a[n_] := Times @@ ((-1)^#[[2]] Binomial[5, #[[2]]] &/@ FactorInteger[n]); Table[a[n], {n, 65}]
PROG
(PARI) for(n=1, 100, print1(direuler(p=2, n, (1 - X)^5)[n], ", ")) \\ Vaclav Kotesovec, Feb 22 2021
KEYWORD
sign,mult
AUTHOR
Ilya Gutkovskiy, Feb 21 2021
STATUS
approved