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

1,4

Links

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

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

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 *)

Prog

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

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.

Sequence in context: A318808 A349935 A257991 * A343029 A343037 A152434

Adjacent sequences: A373589 A373590 A373591 * A373593 A373594 A373595

Keyword

nonn,new

Author

Antti Karttunen, Jun 13 2024

Status

approved