A372785 - OEIS

%I #11 Jan 13 2025 12:29:29

%S 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,

%T 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,

%U 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

%N a(n) = tau(5*n) = A000005(5*n).

%H Antti Karttunen, <a href="/A372785/b372785.txt">Table of n, a(n) for n = 1..20000</a>

%H Vaclav Kotesovec, <a href="/A372785/a372785.jpg">Graph - the asymptotic ratio (100000 terms)</a>

%F 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.

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

%o (PARI) A372785(n) = numdiv(5*n); \\ _Antti Karttunen_, Jan 13 2025

%Y Cf. A283118.

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

%K nonn

%O 1,1

%A _Vaclav Kotesovec_, May 13 2024

%E More terms from _Antti Karttunen_, Jan 13 2025