A351656 Dirichlet g.f.: Product_{p prime} 1 / (1 - p^(-s) - p^(-2*s) - p^(-3*s) - p^(-4*s)).

1, 1, 1, 2, 1, 1, 1, 4, 2, 1, 1, 2, 1, 1, 1, 8, 1, 2, 1, 2, 1, 1, 1, 4, 2, 1, 4, 2, 1, 1, 1, 15, 1, 1, 1, 4, 1, 1, 1, 4, 1, 1, 1, 2, 2, 1, 1, 8, 2, 2, 1, 2, 1, 4, 1, 4, 1, 1, 1, 2, 1, 1, 2, 29, 1, 1, 1, 2, 1, 1, 1, 8, 1, 1, 2, 2, 1, 1, 1, 8, 8, 1, 1, 2, 1, 1, 1

Offset: 1

Author

Ilya Gutkovskiy, Feb 16 2022

Keywords

• nonn
• mult

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• Index entries for sequences computed from exponents in factorization of n.

Crossrefs

Cf. A000078, A351219, A351346, A351347, A351348, A351655.

Programs

Mathematica

t[e_] := t[e] = If[e < 5, 2^(e-1), t[e-1] + t[e-2] + t[e-3] + t[e-4]]; a[1] = 1; a[n_] := Times @@ t /@ Last @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Oct 23 2023 *)

PARI

for(n=1, 87, print1(direuler(p=2, n, 1/(1 - X - X^2 - X^3 - X^4))[n], ", "))

Formula

Multiplicative with a(p^e) = A000078(e+3).