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

Author

Benoit Cloitre, Sep 07 2002

Keywords

• nonn

Links

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

Crossrefs

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

Programs

Mathematica

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

PARI

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

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