A074794 Number of numbers k <= n such that tau(k) == 1 (mod 3) where tau(k) = A000005(k) is the number of divisors of k.

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

Offset

1,6

Links

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

Formula

a(n) is asymptotic to c*n with c = 0.36....

The constant is conjecturally 3*zeta(3)/Pi^2 = 0.3653814847007... (A346602). See A211337 for more details. - Amiram Eldar, Feb 01 2025

Mathematica

Accumulate[Table[Boole[Mod[DivisorSigma[0, n], 3] == 1], {n, 1, 100}]] (* Amiram Eldar, Aug 29 2020 *)

Prog

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

Crossrefs

Cf. A000005, A074795, A074796, A211337, A346602.

Sequence in context: A285879 A117695 A375502 * A234309 A306921 A048686

Adjacent sequences: A074791 A074792 A074793 * A074795 A074796 A074797

Keyword

nonn

Author

Benoit Cloitre, Sep 07 2002

Status

approved