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%I #12 Jun 17 2024 07:11:17
%S 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,
%T 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,
%U 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
%N Number of primes congruent to 1 modulo 3 dividing n (with multiplicity).
%H Antti Karttunen, <a href="/A373591/b373591.txt">Table of n, a(n) for n = 1..100000</a>
%F a(n) = A001222(A248909(n)).
%F a(n) = A001222(n) - (A007949(n)+A373592(n)).
%F 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
%t 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 *)
%o (PARI) A373591(n) = sum(i=1, #n=factor(n)~, (1==n[1, i]%3)*n[2, i]); \\ After code in A083025
%Y Cf. A001222, A007949, A248909, A373592.
%Y Cf. also A065339, A083025.
%K nonn,changed
%O 1,49
%A _Antti Karttunen_, Jun 13 2024
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