A372785 a(n) = tau(5*n) = A000005(5*n).

2, 4, 4, 6, 3, 8, 4, 8, 6, 6, 4, 12, 4, 8, 6, 10, 4, 12, 4, 9, 8, 8, 4, 16, 4, 8, 8, 12, 4, 12, 4, 12, 8, 8, 6, 18, 4, 8, 8, 12, 4, 16, 4, 12, 9, 8, 4, 20, 6, 8, 8, 12, 4, 16, 6, 16, 8, 8, 4, 18, 4, 8, 12, 14, 6, 16, 4, 12, 8, 12, 4, 24, 4, 8, 8, 12, 8, 16, 4, 15, 10, 8, 4, 24, 6, 8, 8, 16, 4, 18, 8, 12, 8, 8, 6

Offset: 1

Author

Vaclav Kotesovec, May 13 2024

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..20000
• Vaclav Kotesovec, Graph - the asymptotic ratio (100000 terms)

Crossrefs

Cf. A283118.

Cf. A000005, A099777, A372713, A372784, A372786, A372787, A372788, A372789, A372790, A372791, A372792.

Programs

Mathematica

Table[DivisorSigma[0, 5*n], {n, 1, 150}]

PARI

A372785(n) = numdiv(5*n); \\ Antti Karttunen, Jan 13 2025

Formula

Sum_{k=1..n} a(k) ~ (9*n*(log(n) + 2*gamma - 1) + n*log(5)) / 5, where gamma is the Euler-Mascheroni constant A001620.

Extensions

More terms from Antti Karttunen, Jan 13 2025