A360911 Multiplicative with a(p^e) = 3*e - 2.

1, 1, 1, 4, 1, 1, 1, 7, 4, 1, 1, 4, 1, 1, 1, 10, 1, 4, 1, 4, 1, 1, 1, 7, 4, 1, 7, 4, 1, 1, 1, 13, 1, 1, 1, 16, 1, 1, 1, 7, 1, 1, 1, 4, 4, 1, 1, 10, 4, 4, 1, 4, 1, 7, 1, 7, 1, 1, 1, 4, 1, 1, 4, 16, 1, 1, 1, 4, 1, 1, 1, 28, 1, 1, 4, 4, 1, 1, 1, 10, 10, 1, 1, 4

Offset: 1

Author

Vaclav Kotesovec, Feb 25 2023

Keywords

• nonn
• mult

Links

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

Crossrefs

Cf. A048785, A226602, A360909, A360910.

Programs

Mathematica

a[n_] := Times @@ ((3*Last[#] - 2) & /@ FactorInteger[n]); a[1] = 1; Array[a, 100] (* Amiram Eldar, Feb 25 2023 *)

PARI

for(n=1, 100, print1(direuler(p=2, n, (1-X+3*X^2)/(1-X)^2)[n], ", "))

Formula

Dirichlet g.f.: zeta(s)^2 * Product_{primes p} (1 - 1/p^s + 3/p^(2*s)).

Dirichlet g.f.: zeta(s) * Product_{primes p} (1 + 3/(p^s*(p^s-1))).

Sum_{k=1..n} a(k) ~ c*n, where c = Product_{primes p} (1 + 3/(p*(p-1))) = 5.092999766083306437144607885642959667401184716827970969797879646796872425...