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Number of divisors of 6n; a(n) = tau(6*n) = A000005(6*n).
11

%I #11 Jul 19 2024 13:29:26

%S 4,6,6,8,8,9,8,10,8,12,8,12,8,12,12,12,8,12,8,16,12,12,8,15,12,12,10,

%T 16,8,18,8,14,12,12,16,16,8,12,12,20,8,18,8,16,16,12,8,18,12,18,12,16,

%U 8,15,16,20,12,12,8,24,8,12,16,16,16,18,8,16,12,24,8,20

%N Number of divisors of 6n; a(n) = tau(6*n) = A000005(6*n).

%H Antti Karttunen, <a href="/A372786/b372786.txt">Table of n, a(n) for n = 1..65537</a>

%H Vaclav Kotesovec, <a href="/A372786/a372786.jpg">Graph - the asymptotic ratio (100000 terms)</a>

%F Sum_{k=1..n} a(k) ~ (15*n*(log(n) + 2*gamma - 1) + n*(5*log(2) + 3*log(3))) / 6, where gamma is the Euler-Mascheroni constant A001620.

%t Table[DivisorSigma[0, 6*n], {n, 1, 150}]

%o (PARI) A372786(n) = numdiv(6*n); \\ _Antti Karttunen_, Jul 19 2024

%Y Cf. A224613.

%Y Cf. A000005, A001620, A099777, A372713, A372784, A372785, A372787, A372788, A372789, A372790, A372791, A372792.

%K nonn

%O 1,1

%A _Vaclav Kotesovec_, May 13 2024