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A373592
Number of primes congruent to 2 modulo 3 dividing n (with multiplicity).
7
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
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. 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
KEYWORD
nonn
AUTHOR
Antti Karttunen, Jun 13 2024
STATUS
approved