login

Reminder: The OEIS is hiring a new managing editor, and the application deadline is January 26.

Dirichlet g.f.: zeta(6*s) / (zeta(s) * zeta(2*s) * zeta(3*s)).
2

%I #10 Nov 30 2020 03:57:52

%S 1,-1,-1,-1,-1,1,-1,0,-1,1,-1,1,-1,1,1,1,-1,1,-1,1,1,1,-1,0,-1,1,0,1,

%T -1,-1,-1,1,1,1,1,1,-1,1,1,0,-1,-1,-1,1,1,1,-1,-1,-1,1,1,1,-1,0,1,0,1,

%U 1,-1,-1,-1,1,1,0,1,-1,-1,1,1,-1,-1,0,-1,1,1,1,1,-1,-1,-1,1,1,-1,-1,1,1,1,0,-1,-1,1,1,1,1,1,-1,-1,1,1,1

%N Dirichlet g.f.: zeta(6*s) / (zeta(s) * zeta(2*s) * zeta(3*s)).

%C Dirichlet inverse of A005361.

%H Amiram Eldar, <a href="/A332732/b332732.txt">Table of n, a(n) for n = 1..10000</a>

%H Ilya Gutkovskiy, <a href="/A332732/a332732.jpg">Scatterplot of partial sums of A332732</a>

%F a(1) = 1; a(n) = -Sum_{d|n, d<n} A005361(n/d) * a(d).

%F a(n) = Sum_{d|n} A007427(n/d) * A299406(d).

%F Multiplicative with a(p^e) = A163810(e). - _Amiram Eldar_, Nov 30 2020

%t a[1] = 1; a[n_] := -Sum[If[d < n, Times @@ (#[[2]] & /@ FactorInteger[n/d]) a[d], 0], {d, Divisors[n]}]; Table[a[n], {n, 1, 100}]

%Y Cf. A005361, A007427, A112526, A163810, A299406, A325126.

%K sign,mult

%O 1

%A _Ilya Gutkovskiy_, Feb 21 2020