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 A354770 #23 Sep 22 2022 01:40:09
%S A354770 2,60,120,180,240,360,720,840,1260,1680,2520,5040,7560,10080,15120,
%T A354770 20160,25200,27720,50400,55440,83160,110880,166320,221760,277200,
%U A354770 332640,498960,554400,665280,720720,1081080,1441440,2162160,2882880,3603600,4324320,6486480,7207200,8648640
%N A354770 Numbers k such that d(k)/log(k) sets a new record, where d(k) is the number-of-divisors function A000005(k).
%C A354770 A related sequence, not yet in the OEIS, is "Numbers k such that log(d(k))/log(k) > log(d(m))/log(m) for all m > k". It begins 2, 4, 6, 12, 24, 36, 60, 72, 120, 180, 240, 360, 420, 720, 840, 1260, 1680, 2520, 5040, 7560, ..., and up to this point it agrees with A236021 (except that it doesn't include 1). Does it continue to agree with A236021?
%D A354770 David desJardins, Posting to Math Fun Mailing List, Jun 22 2022.
%e A354770 The values of d(k)/log(k) for k = 2, 3, ... are 2.885390082, 1.820478453, 2.164042562, 1.242669869, 2.232442506, 1.027796685, 1.923593388, 1.365358840, 1.737177928, 0.8340647828, ... and reach record highs at k = 2 (2.885390082...), k = 60 (2.930872040...), and so on.
%t A354770 s = {}; rm = 0; Do[If[(r = DivisorSigma[0, n]/Log[n]) > rm, rm = r; AppendTo[s, n]], {n, 2, 10^5}]; s (* _Amiram Eldar_, Jun 22 2022 *)
%Y A354770 Cf. A000005, A066523, A236020, A236021, A354768, A354369.
%K A354770 nonn
%O A354770 1,1
%A A354770 _N. J. A. Sloane_, Jun 22 2022
%E A354770 More terms from _Amiram Eldar_, Jun 22 2022