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Dirichlet g.f.: 1 / zeta(s)^5.
8

%I #13 Sep 01 2021 03:09:31

%S 1,-5,-5,10,-5,25,-5,-10,10,25,-5,-50,-5,25,25,5,-5,-50,-5,-50,25,25,

%T -5,50,10,25,-10,-50,-5,-125,-5,-1,25,25,25,100,-5,25,25,50,-5,-125,

%U -5,-50,-50,25,-5,-25,10,-50,25,-50,-5,50,25,50,25,25,-5,250,-5,25,-50,0,25

%N Dirichlet g.f.: 1 / zeta(s)^5.

%C Dirichlet inverse of A061200.

%H Seiichi Manyama, <a href="/A341831/b341831.txt">Table of n, a(n) for n = 1..10000</a>

%F Multiplicative with a(p^e) = (-1)^e * binomial(5, e).

%F a(1) = 1; a(n) = -Sum_{d|n, d < n} tau_5(n/d) * a(d).

%t a[1] = 1; a[n_] := Times @@ ((-1)^#[[2]] Binomial[5, #[[2]]] &/@ FactorInteger[n]); Table[a[n], {n, 65}]

%o (PARI) for(n=1, 100, print1(direuler(p=2, n, (1 - X)^5)[n], ", ")) \\ _Vaclav Kotesovec_, Feb 22 2021

%Y Row 5 of A346148.

%Y Cf. A007427, A007428, A008683, A061200, A247343, A341832, A341833, A341834, A341835, A341836.

%K sign,mult

%O 1,2

%A _Ilya Gutkovskiy_, Feb 21 2021