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

%I #6 May 13 2024 12:21:42

%S 4,6,8,8,6,12,8,10,12,9,8,16,8,12,12,12,8,18,8,12,16,12,8,20,8,12,16,

%T 16,8,18,8,14,16,12,12,24,8,12,16,15,8,24,8,16,18,12,8,24,12,12,16,16,

%U 8,24,12,20,16,12,8,24,8,12,24,16,12,24,8,16,16,18,8,30

%N a(n) = tau(10*n) = A000005(10*n).

%H Vaclav Kotesovec, <a href="/A372790/a372790.jpg">Graph - the asymptotic ratio (100000 terms)</a>

%F Sum_{k=1..n} a(k) ~ (27*n*(log(n) + 2*gamma - 1) + n*(9*log(2) + 3*log(5))) / 10, where gamma is the Euler-Mascheroni constant A001620.

%t Table[DivisorSigma[0, 10*n], {n, 1, 150}]

%Y Cf. A000005, A099777, A372713, A372784, A372785, A372786, A372787, A372788, A372789, A372791, A372792.

%K nonn

%O 1,1

%A _Vaclav Kotesovec_, May 13 2024