A391793 - OEIS

%I #9 Dec 28 2025 20:36:24

%S 1,0,0,-1,0,0,0,-1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,-1,0,0,0,0,2,

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

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

%N Multiplicative sequence a(n) with a(p^e) = ((e mod 5) * ((e mod 5) - 5) + 4) / 2 for prime p and e > 0.

%F Dirichlet g.f.: zeta(5*s) / (zeta(2*s) * zeta(3*s)).

%t f[p_, e_] := Module[{r = Mod[e, 5]}, (r*(r-5) + 4)/2]; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* _Amiram Eldar_, Dec 20 2025 *)

%o (PARI) a(n) = factorback(apply(e->((e%5)*((e%5)-5)+4)/2,factor(n)[, 2]))

%o (Python)

%o from math import prod

%o from sympy import factorint

%o def A391793(n): return prod((2,0,-1,-1,0)[e%5] for e in factorint(n).values()) # _Chai Wah Wu_, Dec 28 2025

%K sign,easy,mult

%O 1,32

%A _Werner Schulte_, Dec 20 2025