A356005 Number of integers k such that k*tau(k) <= n.

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

Offset: 1

Author

Benoit Cloitre, Jul 22 2022

Keywords

• nonn

Comments

Partial sums of A327166. - Rémy Sigrist, Jul 23 2022

Links

• R. Balasubramanian and K. Ramachandra, On the number of integers n such that nd(n)<=x, Acta Arith., 49 (1988), 313-322.
• Vaclav Kotesovec, Plot of a(n) / (n/sqrt(log(n))) for n = 1..10^7

Crossrefs

Cf. A038040, A327166.

Programs

Mathematica

Table[Sum[If[k*DivisorSigma[0, k] <= n, 1, 0], {k, 1, n}], {n, 1, 100}] (* Vaclav Kotesovec, Jul 23 2022 *)

PARI

a(n)=sum(k=1,n,if(k*numdiv(k)<=n,1,0))

Formula

a(n) is asymptotic to C*n/sqrt(log(n)) for a suitable constant C > 0.