A373592 Number of primes congruent to 2 modulo 3 dividing n (with multiplicity).

0, 1, 0, 2, 1, 1, 0, 3, 0, 2, 1, 2, 0, 1, 1, 4, 1, 1, 0, 3, 0, 2, 1, 3, 2, 1, 0, 2, 1, 2, 0, 5, 1, 2, 1, 2, 0, 1, 0, 4, 1, 1, 0, 3, 1, 2, 1, 4, 0, 3, 1, 2, 1, 1, 2, 3, 0, 2, 1, 3, 0, 1, 0, 6, 1, 2, 0, 3, 1, 2, 1, 3, 0, 1, 2, 2, 1, 1, 0, 5, 0, 2, 1, 2, 2, 1, 1, 4, 1, 2, 0, 3, 0, 2, 1, 5, 0, 1, 1, 4, 1, 2, 0, 3, 1

Offset: 1

Author

Antti Karttunen, Jun 13 2024

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..100000

Crossrefs

Cf. A001222, A343430, A373591.

Cf. also A065339, A083025.

Differs from A257991 for the first time at n=29, where a(29) = 1, while A257991(29) = 0.

Programs

Mathematica

f[p_, e_] := If[Mod[p, 3] == 2, e, 0]; f[3, e_] := 0; a[1] = 0; a[n_] := Plus @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Jun 17 2024 *)

PARI

A373592(n) = sum(i=1, #n=factor(n)~, (2==n[1, i]%3)*n[2, i]); \\ After code in A083025

Formula

a(n) = A001222(A343430(n)).

a(n) = A001222(n) - (A007949(n)+A373591(n)).

Totally additive with a(3) = 0, a(p) = 1 if p == 2 (mod 3), and a(p) = 0 if p == 1 (mod 3). - Amiram Eldar, Jun 17 2024