A383717 Dirichlet g.f.: Product_{p prime} (1 + 1/p^(s-1) + 1/p^(2*s-1)).

1, 2, 3, 2, 5, 6, 7, 0, 3, 10, 11, 6, 13, 14, 15, 0, 17, 6, 19, 10, 21, 22, 23, 0, 5, 26, 0, 14, 29, 30, 31, 0, 33, 34, 35, 6, 37, 38, 39, 0, 41, 42, 43, 22, 15, 46, 47, 0, 7, 10, 51, 26, 53, 0, 55, 0, 57, 58, 59, 30, 61, 62, 21, 0, 65, 66, 67, 34, 69, 70, 71, 0, 73

Offset

1,2

Links

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

Formula

Sum_{k=1..n} a(k) ~ c * n^2/2, where c = Product_{p prime} (1 - 1/p^2 + 1/p^3 - 1/p^4) = 0.684286924186862318141968725791218083472312736723163777284618226290055...

Multiplicative with a(p^e) = p is e <= 2, and 0 otherwise. - Amiram Eldar, May 07 2025

Mathematica

f[p_, e_] := If[e < 3, p, 0]; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, May 07 2025 *)

Prog

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

Crossrefs

Cf. A007947, A056552, A335341, A336649.

Sequence in context: A088631 A086184 A363484 * A056552 A049273 A389365

Adjacent sequences: A383714 A383715 A383716 * A383718 A383719 A383720

Keyword

nonn,mult,easy

Author

Vaclav Kotesovec, May 07 2025

Status

approved