A372786 Number of divisors of 6n; a(n) = tau(6*n) = A000005(6*n).

4, 6, 6, 8, 8, 9, 8, 10, 8, 12, 8, 12, 8, 12, 12, 12, 8, 12, 8, 16, 12, 12, 8, 15, 12, 12, 10, 16, 8, 18, 8, 14, 12, 12, 16, 16, 8, 12, 12, 20, 8, 18, 8, 16, 16, 12, 8, 18, 12, 18, 12, 16, 8, 15, 16, 20, 12, 12, 8, 24, 8, 12, 16, 16, 16, 18, 8, 16, 12, 24, 8, 20

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. A224613.

Cf. A000005, A001620, A099777, A372713, A372784, A372785, A372787, A372788, A372789, A372790, A372791, A372792.

Programs

Mathematica

Table[DivisorSigma[0, 6*n], {n, 1, 150}]

PARI

A372786(n) = numdiv(6*n); \\ Antti Karttunen, Jul 19 2024

Formula

Sum_{k=1..n} a(k) ~ (15*n*(log(n) + 2*gamma - 1) + n*(5*log(2) + 3*log(3))) / 6, where gamma is the Euler-Mascheroni constant A001620.