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 A356573 #70 Dec 12 2022 09:38:41
%S A356573 1,2,4,6,12,24,60,120,240,360,720,840,1260,1680,2520,5040,10080,15120,
%T A356573 27720,55440,110880,166320,277200,332640,554400,720720,1441440,
%U A356573 2162160,3603600,4324320,7207200,10810800,21621600,36756720,61261200,73513440,122522400,183783600
%N A356573 Sigma-dense numbers: integers k such that sigma(k) * log(1+log(1+log(1+k))) / (k * log(1+log(1+k))) sets a new record.
%C A356573 This sequence is to A210594 (the generalization in the latter's comment section) as sigma (A000203, the sum of divisors function) is to tau (A000005, the number of divisors function).
%t A356573 s={}; dm = 0; Do[If[(d = DivisorSigma[1, n] * Log[1 + Log[1 + Log[1 + n]]] / (n * Log[1 + Log[1 + n]])) > dm, dm = d; AppendTo[s, n]], {n, 1, 10^5}]; s (* _Amiram Eldar_, Dec 12 2022 *)
%o A356573 (PARI) listas(nn) = {my(m=0); for (k=1, nn, my(mm = sigma(k)*log(1+log(1+log(1+k))) / (k * log(1+log(1+k)))); if (mm > m, print1(k, ", "); m = mm); ); } \\ _Michel Marcus_, Dec 12 2022
%Y A356573 Cf. A000005, A000203, A210594.
%K A356573 nonn
%O A356573 1,2
%A A356573 _Hal M. Switkay_, Dec 11 2022
%E A356573 a(22)-a(31) from _Michel Marcus_, Dec 12 2022
%E A356573 a(32)-a(38) from _Amiram Eldar_, Dec 12 2022