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

Author

N. J. A. Sloane

Keywords

• nonn

Links

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

Crossrefs

Cf. A001221, A005074, A005088, A079978.

Programs

Mathematica

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

Scheme

(define (A005090 n) (if (= 1 n) 0 (+ (A004526 (modulo (A020639 n) 3)) (A005090 (A028234 n))))) ;; Antti Karttunen, Jul 10 2017

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)

Extensions

More terms from Antti Karttunen, Jul 10 2017