A074796 Number of numbers k <= n such that tau(k) == 2 (mod 3) where tau(k) = A000005(k) is the number of divisors of k.

0, 1, 2, 2, 3, 3, 4, 4, 4, 4, 5, 5, 6, 6, 6, 7, 8, 8, 9, 9, 9, 9, 10, 11, 11, 11, 11, 11, 12, 13, 14, 14, 14, 14, 14, 14, 15, 15, 15, 16, 17, 18, 19, 19, 19, 19, 20, 20, 20, 20, 20, 20, 21, 22, 22, 23, 23, 23, 24, 24, 25, 25, 25, 25, 25, 26, 27, 27, 27, 28, 29, 29, 30, 30, 30, 30

Offset

1,3

Links

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

Formula

a(n) is asymptotic to c*n with c = 0.38....

The constant is conjecturally 3*zeta(3)/Pi^2 = 0.3653814847007... (A346602). See A211338 for more details. - Amiram Eldar, Feb 01 2025

Mathematica

Accumulate[Table[If[Mod[DivisorSigma[0, n], 3]==2, 1, 0], {n, 80}]] (* Harvey P. Dale, Apr 22 2018 *)

Prog

(PARI) a(n)=sum(k=1, n, if(numdiv(k)%3-2, 0, 1))

Crossrefs

Cf. A000005, A074794, A074795, A211338, A346602.

Sequence in context: A070549 A255574 A283992 * A061070 A285879 A117695

Adjacent sequences: A074793 A074794 A074795 * A074797 A074798 A074799

Keyword

nonn

Author

Benoit Cloitre, Sep 07 2002

Status

approved