A372789 Number of divisors of 9n; a(n) = tau(9*n) = A000005(9*n).

3, 6, 4, 9, 6, 8, 6, 12, 5, 12, 6, 12, 6, 12, 8, 15, 6, 10, 6, 18, 8, 12, 6, 16, 9, 12, 6, 18, 6, 16, 6, 18, 8, 12, 12, 15, 6, 12, 8, 24, 6, 16, 6, 18, 10, 12, 6, 20, 9, 18, 8, 18, 6, 12, 12, 24, 8, 12, 6, 24, 6, 12, 10, 21, 12, 16, 6, 18, 8, 24, 6, 20, 6, 12, 12

Offset: 1

Author

Vaclav Kotesovec, May 13 2024

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537
• Vaclav Kotesovec, Graph - the asymptotic ratio (100000 terms)

Crossrefs

Cf. A283123.

Cf. A000005, A099777, A372713, A372784, A372785, A372786, A372787, A372788, A372790, A372791, A372792.

Programs

Mathematica

Table[DivisorSigma[0, 9*n], {n, 1, 150}]

PARI

A372789(n) = numdiv(9*n); \\ Antti Karttunen, Jul 19 2024

Formula

Sum_{k=1..n} a(k) ~ (21*n*(log(n) + 2*gamma - 1) + n*6*log(3)) / 9, where gamma is the Euler-Mascheroni constant A001620.