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A351521
Dirichlet g.f.: Product_{p prime} (1 + 4*p^(-s)).
2
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
1,2
LINKS
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
MATHEMATICA
Table[MoebiusMu[n]^2 * 4^PrimeNu[n], {n, 1, 100}]
PROG
(PARI) for(n=1, 100, print1(direuler(p=2, n, (1 + 4*X))[n], ", "))
CROSSREFS
KEYWORD
nonn,mult
AUTHOR
Vaclav Kotesovec, Feb 17 2022
STATUS
approved