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 A372674 #27 May 13 2024 03:50:30
%S A372674 1,8,23,54,89,162,221,326,439,596,707,964,1107,1352,1645,1976,2179,
%T A372674 2630,2865,3390,3859,4316,4615,5406,5883,6444,7059,7892,8299,9430,
%U A372674 9877,10794,11635,12424,13361,14852,15415,16324,17349,18952,19587,21342,22017,23486,25177
%N A372674 a(n) = Sum_{j=1..n} Sum_{k=1..n} tau(j*k).
%C A372674 For m>=1, Sum_{j=1..n} tau(m*j) = A018804(m) * n * log(n) + O(n).
%C A372674 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 A372674 Vaclav Kotesovec, <a href="/A372674/b372674.txt">Table of n, a(n) for n = 1..10000</a>
%H A372674 Vaclav Kotesovec, <a href="/A372674/a372674.jpg">Plot of a(n) / (n^2 * (log(n) + 2*gamma - 1/2)^2) for n = 1..100000</a>
%t A372674 Table[Sum[DivisorSigma[0, j*k], {j, 1, n}, {k, 1, n}], {n, 1, 50}]
%t A372674 s = 1; Join[{1}, Table[s += DivisorSigma[0, n^2] + 2*Sum[DivisorSigma[0, j*n], {j, 1, n - 1}], {n, 2, 50}]]
%Y A372674 Cf. A372633, A372675.
%Y A372674 Cf. A006218, A263086.
%Y A372674 cf. A000005, A099777, A372713.
%K A372674 nonn
%O A372674 1,2
%A A372674 _Vaclav Kotesovec_, May 10 2024