A074795 Number of numbers k <= n such that tau(k) == 0 (mod 3) where tau(k) = A000005(k) is the number of divisors of k.

0, 0, 0, 1, 1, 1, 1, 1, 2, 2, 2, 3, 3, 3, 3, 3, 3, 4, 4, 5, 5, 5, 5, 5, 6, 6, 6, 7, 7, 7, 7, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 10, 11, 11, 11, 11, 12, 13, 13, 14, 14, 14, 14, 14, 14, 14, 14, 15, 15, 15, 16, 16, 16, 16, 16, 17, 17, 17, 17, 18, 18, 18, 19, 20, 20, 20, 20, 20, 20, 20, 20, 21

Offset

1,9

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

L. G. Sathe, On a congruence property of the divisor function, American Journal of Mathematics, Vol. 67, No. 3 (1945), pp. 397-406.

Formula

a(n) is asymptotic to c*n with c = 0.26....

The constant is c = 1 - zeta(3)/zeta(2) = 1 - 6*zeta(3)/Pi^2 = 0.2692370305 ... (Sathe, 1945). - Amiram Eldar, Aug 29 2020

Mathematica

Accumulate[Boole[Divisible[DivisorSigma[0, Range[90]], 3]]] (* Harvey P. Dale, Jan 11 2015 *)

Prog

(PARI) a(n)=sum(k=1, n, if(numdiv(k)%3, 0, 1))

Crossrefs

Cf. A000005, A059269, A074794, A074796.

Sequence in context: A156684 A070564 A072358 * A069577 A282426 A318781

Adjacent sequences: A074792 A074793 A074794 * A074796 A074797 A074798

Keyword

nonn

Author

Benoit Cloitre, Sep 07 2002

Status

approved