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

Author

Benoit Cloitre, Sep 07 2002

Keywords

• nonn

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.

Crossrefs

Cf. A000005, A059269, A074794, A074796.

Programs

Mathematica

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

PARI

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

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