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Number of divisors of 9n; a(n) = tau(9*n) = A000005(9*n).
11

%I #10 Jul 19 2024 13:29:37

%S 3,6,4,9,6,8,6,12,5,12,6,12,6,12,8,15,6,10,6,18,8,12,6,16,9,12,6,18,6,

%T 16,6,18,8,12,12,15,6,12,8,24,6,16,6,18,10,12,6,20,9,18,8,18,6,12,12,

%U 24,8,12,6,24,6,12,10,21,12,16,6,18,8,24,6,20,6,12,12

%N Number of divisors of 9n; a(n) = tau(9*n) = A000005(9*n).

%H Antti Karttunen, <a href="/A372789/b372789.txt">Table of n, a(n) for n = 1..65537</a>

%H Vaclav Kotesovec, <a href="/A372789/a372789.jpg">Graph - the asymptotic ratio (100000 terms)</a>

%F Sum_{k=1..n} a(k) ~ (21*n*(log(n) + 2*gamma - 1) + n*6*log(3)) / 9, where gamma is the Euler-Mascheroni constant A001620.

%t Table[DivisorSigma[0, 9*n], {n, 1, 150}]

%o (PARI) A372789(n) = numdiv(9*n); \\ _Antti Karttunen_, Jul 19 2024

%Y Cf. A283123.

%Y Cf. A000005, A099777, A372713, A372784, A372785, A372786, A372787, A372788, A372790, A372791, A372792.

%K nonn

%O 1,1

%A _Vaclav Kotesovec_, May 13 2024