This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A372792 #15 Jan 15 2025 09:17:16
%S A372792 6,8,9,10,12,12,12,12,12,16,12,15,12,16,18,14,12,16,12,20,18,16,12,18,
%T A372792 18,16,15,20,12,24,12,16,18,16,24,20,12,16,18,24,12,24,12,20,24,16,12,
%U A372792 21,18,24,18,20,12,20,24,24,18,16,12,30,12,16,24,18,24,24
%N A372792 Number of divisors of 12n; a(n) = tau(12*n) = A000005(12*n).
%C A372792 In general, for m>=1, Sum_{j=1..n} tau(m*j) = A018804(m) * n * log(n) + O(n).
%C A372792 If p is prime, then Sum_{j=1..n} tau(p*j) ~ (2*p - 1) * n * (log(n) - 1 + 2*gamma)/p + n*log(p)/p, where gamma is the Euler-Mascheroni constant A001620.
%H A372792 Antti Karttunen, <a href="/A372792/b372792.txt">Table of n, a(n) for n = 1..20000</a>
%H A372792 Vaclav Kotesovec, <a href="/A372792/a372792.jpg">Graph - the asymptotic ratio (100000 terms)</a>
%F A372792 Sum_{k=1..n} a(k) ~ (40*n*(log(n) + 2*gamma - 1) + n*(20*log(2) + 8*log(3))) / 12, where gamma is the Euler-Mascheroni constant A001620.
%t A372792 Table[DivisorSigma[0, 12*n], {n, 1, 150}]
%o A372792 (PARI) A372792(n) = numdiv(12*n); \\ _Antti Karttunen_, Jul 19 2024
%Y A372792 Cf. A000005, A099777, A372713, A372784, A372785, A372786, A372787, A372788, A372789, A372790, A372791.
%K A372792 nonn
%O A372792 1,1
%A A372792 _Vaclav Kotesovec_, May 13 2024