A373591 Number of primes congruent to 1 modulo 3 dividing n (with multiplicity).

0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 2, 0, 1, 0, 1, 0, 1, 2, 0, 0, 0, 0, 1, 1, 1

Offset

1,49

Links

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

Formula

a(n) = A001222(A248909(n)).

a(n) = A001222(n) - (A007949(n)+A373592(n)).

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

Mathematica

f[p_, e_] := If[Mod[p, 3] == 1, 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) A373591(n) = sum(i=1, #n=factor(n)~, (1==n[1, i]%3)*n[2, i]); \\ After code in A083025

Crossrefs

Cf. A001222, A007949, A248909, A373592.

Cf. also A065339, A083025.

Sequence in context: A277885 A333842 A334109 * A374099 A109527 A373241

Adjacent sequences: A373588 A373589 A373590 * A373592 A373593 A373594

Keyword

nonn

Author

Antti Karttunen, Jun 13 2024

Status

approved