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%I #28 Apr 14 2021 22:23:48
%S 0,1,0,1,1,1,0,1,0,2,1,1,0,1,1,1,1,1,0,2,0,2,1,1,1,1,0,1,1,2,0,1,1,2,
%T 1,1,0,1,0,2,1,1,0,2,1,2,1,1,0,2,1,1,1,1,2,1,0,2,1,2,0,1,0,1,1,2,0,2,
%U 1,2,1,1,0,1,1,1,1,1,0,2,0,2,1,1,2,1,1,2,1,2,0,2,0,2,1,1,0,1,1,2,1,2,0,1,1,2,1,1,0,3,0,1,1,1,2,2,0,2,1,2
%N Number of primes == 2 mod 3 dividing n.
%H Antti Karttunen, <a href="/A005090/b005090.txt">Table of n, a(n) for n = 1..10000</a>
%F Additive with a(p^e) = 1 if p = 2 (mod 3), 0 otherwise.
%F From _Antti Karttunen_, Jul 10 2017: (Start)
%F a(1) = 0; for n > 1, floor((A020639(n) mod 3)/2) + a(A028234(n)).
%F a(n) = A001221(n) - A005088(n) - A079978(n).
%F (End)
%t Array[DivisorSum[#, 1 &, And[PrimeQ@ #, Mod[#, 3] == 2] &] &, 120] (* _Michael De Vlieger_, Jul 11 2017 *)
%o (Scheme) (define (A005090 n) (if (= 1 n) 0 (+ (A004526 (modulo (A020639 n) 3)) (A005090 (A028234 n))))) ;; _Antti Karttunen_, Jul 10 2017
%o (PARI) a(n) = my(f=factor(n)); sum(k=1, #f~, (f[k,1] % 3) == 2); \\ _Michel Marcus_, Jul 11 2017
%o (Python)
%o from sympy import primefactors
%o def a(n): return sum(1 for p in primefactors(n) if p%3==2)
%o print([a(n) for n in range(1, 101)]) # _Indranil Ghosh_, Jul 11 2017
%Y Cf. A001221, A005074, A005088, A079978.
%K nonn
%O 1,10
%A _N. J. A. Sloane_
%E More terms from _Antti Karttunen_, Jul 10 2017
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