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A381642 Numbers k such that F(k) > F(m) for all m < k, where F(k) = A381641(k)/A381639(k).

%I A381642 #6 Mar 03 2025 13:34:10
%S A381642 1,6,10,14,22,26,34,38,42,46,58,62,66,78,102,114,130,170,190,230,290,
%T A381642 310,370,406,410,430,434,470,518,574,602,658,742,826,854,938,994,1022,
%U A381642 1106,1162,1218,1302,1554,1722,1806,1974,2226,2478,2562,2706,2814,2838,2982
%N A381642 Numbers k such that F(k) > F(m) for all m < k, where F(k) = A381641(k)/A381639(k).
%C A381642 Called "F-champion numbers" by Erdős and Nicolas (1989).
%C A381642 All the terms are squarefree numbers.
%H A381642 Amiram Eldar, <a href="/A381642/b381642.txt">Table of n, a(n) for n = 1..3000</a>
%H A381642 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 A381642 f[n_] := Module[{p = FactorInteger[n][[;; , 1]]}, Total[1 - 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[3000]
%o A381642 (PARI) f(n) = {my(p = factor(n)[,1]); sum(i = 1, #p-1, 1 - p[i]/p[i+1]);}
%o A381642 list(lim) = {my(fm = -1, f1); for(k = 1, lim, f1 = f(k); if(f1 > fm, print1(k, ", "); fm = f1));}
%Y A381642 Cf. A005117, A381639, A381640, A381641.
%K A381642 nonn
%O A381642 1,2
%A A381642 _Amiram Eldar_, Mar 03 2025