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 A112809 #20 Mar 15 2021 01:50:18
%S A112809 1,6,20,21,42,120,342,506,567,594,600,610,2184,4896,6108,6162,6498,
%T A112809 12760,14067,14157,14201,93942,123462,123519,734413,2451397,4591010,
%U A112809 11571129,13346540,13619348,13619790,46180567
%N A112809 Positions of records in A110566.
%t A112809 c = 0; a = h = 1; t = {}; Do[a = LCM[a, n]; h = h + 1/n; b = a/Denominator[h]; If[b > c, c = b; AppendTo[t, n]], {n, 10^6}]; t
%o A112809 (PARI) lista(nn) = {rec = 0; for (n=1, nn, new = lcm(vector(n, k, k))/denominator(sum(k=1, n, 1/k)); if (new > rec, print1(n, ", "); rec = new););} \\ _Michel Marcus_, Mar 07 2018
%Y A112809 Cf. A110566, A001008, A002805, A003418, A025529, A098464, A112810.
%K A112809 more,nonn
%O A112809 1,2
%A A112809 _Robert G. Wilson v_, Sep 19 2005
%E A112809 a(27)-a(28) from _Amiram Eldar_, Dec 18 2018
%E A112809 a(29)-a(31) from _Chai Wah Wu_, Mar 08 2021
%E A112809 a(32) from _Chai Wah Wu_, Mar 14 2021