A360910 Multiplicative with a(p^e) = 3*e - 1.

1, 2, 2, 5, 2, 4, 2, 8, 5, 4, 2, 10, 2, 4, 4, 11, 2, 10, 2, 10, 4, 4, 2, 16, 5, 4, 8, 10, 2, 8, 2, 14, 4, 4, 4, 25, 2, 4, 4, 16, 2, 8, 2, 10, 10, 4, 2, 22, 5, 10, 4, 10, 2, 16, 4, 16, 4, 4, 2, 20, 2, 4, 10, 17, 4, 8, 2, 10, 4, 8, 2, 40, 2, 4, 10, 10, 4, 8, 2

Offset

1,2

Links

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

Formula

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

Let f(s) = Product_{primes p} (1 + 2/p^(2*s)), then Sum_{k=1..n} a(k) ~ n*(f(1)*(log(n) + 2*gamma - 1) + f'(1)), where f(1) = Product_{primes p} (1 + 2/p^2) = 2.1908700855532557963501937947188223715671192999357721091330157224657649571..., f'(1) = f(1) * Sum_{primes p} (-4*log(p)/(p^2 + 2)) = -3.559220569509264750413960031425742000438433285978558703470289340806139902... and gamma is the Euler-Mascheroni constant A001620.

Mathematica

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

Prog

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

Crossrefs

Cf. A048785, A226602, A360909, A360911, A360908.

Sequence in context: A371012 A340839 A257090 * A339664 A124316 A328705

Adjacent sequences: A360907 A360908 A360909 * A360911 A360912 A360913

Keyword

nonn,mult

Author

Vaclav Kotesovec, Feb 25 2023

Status

approved