A391793 Multiplicative sequence a(n) with a(p^e) = ((e mod 5) * ((e mod 5) - 5) + 4) / 2 for prime p and e > 0.

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, 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, 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

Offset

1,32

Links

Table of n, a(n) for n=1..100.

Formula

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

Mathematica

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 *)

Prog

(PARI) a(n) = factorback(apply(e->((e%5)*((e%5)-5)+4)/2, factor(n)[, 2]))
(Python)
from math import prod
from sympy import factorint
def A391793(n): return prod((2, 0, -1, -1, 0)[e%5] for e in factorint(n).values()) # Chai Wah Wu, Dec 28 2025

Crossrefs

Sequence in context: A135468 A003196 A319581 * A393491 A331302 A062977

Adjacent sequences: A391790 A391791 A391792 * A391794 A391795 A391796

Keyword

sign,easy,mult

Author

Werner Schulte, Dec 20 2025

Status

approved