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 A381640 #5 Mar 03 2025 13:33:54
%S A381640 1,6,30,105,210,2310,15015,30030,255255,510510,1939938,3233230,
%T A381640 4849845,9699690,111546435,223092870,3234846615,6469693230
%N A381640 Numbers k such that f(k) > f(m) for all m < k, where f(k) = A381638(k)/A381639(k).
%C A381640 Called "f-champion numbers" by Erdős and Nicolas (1989).
%C A381640 All the terms are squarefree numbers.
%C A381640 The primorial numbers, A002110(k), are all terms for k large enough.
%H A381640 Paul Erdős and Jean-Louis Nicolas, <a href="https://doi.org/10.1515/9783110852790.169">Grandes valeurs de fonctions liées aux diviseurs premiers consécutifs d'un entier</a>, in: Jean-Marie de Koninck and Claude Levesque (eds.), Théorie des nombres / Number Theory, Proceedings of the International Number Theory Conference held at Université Laval, July 5-18, 1987, De Gruyter, 1989; <a href="https://users.renyi.hu/~p_erdos/1989-08.pdf">alternative link</a>.
%t A381640 f[n_] := Module[{p = FactorInteger[n][[;; , 1]]}, Total[Most[p]/Rest[p]]]; seq[lim_] := Module[{fi, fmax = -1, s = {}}, Do[fi = f[i]; If[fi > fmax, fmax = fi; AppendTo[s, i]], {i, 1, lim}]; s]; seq[12000]
%o A381640 (PARI) f(n) = {my(p = factor(n)[,1]); sum(i = 1, #p-1, p[i]/p[i+1]);}
%o A381640 list(lim) = {my(fm = -1, f1); for(k = 1, lim, f1 = f(k); if(f1 > fm, print1(k, ", "); fm = f1));}
%Y A381640 Cf. A002110, A005117, A381638, A381639, A381642.
%K A381640 nonn,more
%O A381640 1,2
%A A381640 _Amiram Eldar_, Mar 03 2025