A005090 Number of primes == 2 mod 3 dividing n.

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, 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, 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

Offset

1,10

Links

Antti Karttunen, Table of n, a(n) for n = 1..10000

Formula

Additive with a(p^e) = 1 if p = 2 (mod 3), 0 otherwise.

From Antti Karttunen, Jul 10 2017: (Start)

a(1) = 0; for n > 1, floor((A020639(n) mod 3)/2) + a(A028234(n)).

a(n) = A001221(n) - A005088(n) - A079978(n).

(End)

Mathematica

Array[DivisorSum[#, 1 &, And[PrimeQ@ #, Mod[#, 3] == 2] &] &, 120] (* Michael De Vlieger, Jul 11 2017 *)

Prog

(Scheme) (define (A005090 n) (if (= 1 n) 0 (+ (A004526 (modulo (A020639 n) 3)) (A005090 (A028234 n))))) ;; Antti Karttunen, Jul 10 2017
(PARI) a(n) = my(f=factor(n)); sum(k=1, #f~, (f[k, 1] % 3) == 2); \\ Michel Marcus, Jul 11 2017
(Python)
from sympy import primefactors
def a(n): return sum(1 for p in primefactors(n) if p%3==2)
print([a(n) for n in range(1, 101)]) # Indranil Ghosh, Jul 11 2017

Crossrefs

Cf. A001221, A005074, A005088, A079978.

Sequence in context: A191904 A265892 A324966 * A073490 A279907 A225654

Adjacent sequences: A005087 A005088 A005089 * A005091 A005092 A005093

Keyword

nonn

Author

N. J. A. Sloane

Extensions

More terms from Antti Karttunen, Jul 10 2017

Status

approved