A351521 Dirichlet g.f.: Product_{p prime} (1 + 4*p^(-s)).

1, 4, 4, 0, 4, 16, 4, 0, 0, 16, 4, 0, 4, 16, 16, 0, 4, 0, 4, 0, 16, 16, 4, 0, 0, 16, 0, 0, 4, 64, 4, 0, 16, 16, 16, 0, 4, 16, 16, 0, 4, 64, 4, 0, 0, 16, 4, 0, 0, 0, 16, 0, 4, 0, 16, 0, 16, 16, 4, 0, 4, 16, 0, 0, 16, 64, 4, 0, 16, 64, 4, 0, 4, 16, 0, 0, 16, 64

Offset: 1

Author

Vaclav Kotesovec, Feb 17 2022

Keywords

• nonn
• mult

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A074823, A347149.

Cf. A061142, A165824, A165825.

Cf. A008966, A035116.

Programs

Mathematica

Table[MoebiusMu[n]^2 * 4^PrimeNu[n], {n, 1, 100}]

PARI

for(n=1, 100, print1(direuler(p=2, n, (1 + 4*X))[n], ", "))

Formula

Dirichlet g.f.: zeta(s)^4 * Product_{prime p} (1 + (4 - 15*p^s + 20*p^(2*s) - 10*p^(3*s))/p^(5*s)).

a(n) = A008966(n) * A035116(n). - Enrique Pérez Herrero, Oct 27 2022

Multiplicative with a(p) = 4, and a(p^e) = 0 for e >= 2. - Amiram Eldar, Dec 25 2022