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a(n) = tau(8*n) = A000005(8*n).
10

%I #6 May 13 2024 12:21:49

%S 4,5,8,6,8,10,8,7,12,10,8,12,8,10,16,8,8,15,8,12,16,10,8,14,12,10,16,

%T 12,8,20,8,9,16,10,16,18,8,10,16,14,8,20,8,12,24,10,8,16,12,15,16,12,

%U 8,20,16,14,16,10,8,24,8,10,24,10,16,20,8,12,16,20,8,21

%N a(n) = tau(8*n) = A000005(8*n).

%H Vaclav Kotesovec, <a href="/A372788/a372788.jpg">Graph - the asymptotic ratio (100000 terms)</a>

%F Sum_{k=1..n} a(k) ~ (20*n*(log(n) + 2*gamma - 1) + n*12*log(2)) / 8, where gamma is the Euler-Mascheroni constant A001620.

%t Table[DivisorSigma[0, 8*n], {n, 1, 150}]

%Y Cf. A283122.

%Y Cf. A000005, A099777, A372713, A372784, A372785, A372786, A372787, A372789, A372790, A372791, A372792.

%K nonn

%O 1,1

%A _Vaclav Kotesovec_, May 13 2024