A341833 - OEIS

%I #12 Sep 01 2021 03:09:12

%S 1,-7,-7,21,-7,49,-7,-35,21,49,-7,-147,-7,49,49,35,-7,-147,-7,-147,49,

%T 49,-7,245,21,49,-35,-147,-7,-343,-7,-21,49,49,49,441,-7,49,49,245,-7,

%U -343,-7,-147,-147,49,-7,-245,21,-147,49,-147,-7,245,49,245,49,49,-7,1029,-7,49

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

%C Dirichlet inverse of A111217.

%H Seiichi Manyama, <a href="/A341833/b341833.txt">Table of n, a(n) for n = 1..10000</a>

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

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

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

%o (PARI) for(n=1, 100, print1(direuler(p=2, n, (1 - X)^7)[n], ", ")) \\ _Vaclav Kotesovec_, Feb 22 2021

%Y Row 7 of A346148.

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

%K sign,mult

%O 1,2

%A _Ilya Gutkovskiy_, Feb 21 2021