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

1, 6, 10, 14, 22, 26, 34, 38, 42, 46, 58, 62, 66, 78, 102, 114, 130, 170, 190, 230, 290, 310, 370, 406, 410, 430, 434, 470, 518, 574, 602, 658, 742, 826, 854, 938, 994, 1022, 1106, 1162, 1218, 1302, 1554, 1722, 1806, 1974, 2226, 2478, 2562, 2706, 2814, 2838, 2982

Offset: 1

Author

Amiram Eldar, Mar 03 2025

Keywords

• nonn

Comments

Called "F-champion numbers" by Erdős and Nicolas (1989).

All the terms are squarefree numbers.

Links

• Amiram Eldar, Table of n, a(n) for n = 1..3000
• Paul Erdős and Jean-Louis Nicolas, Grandes valeurs de fonctions liées aux diviseurs premiers consécutifs d'un entier, 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; alternative link.

Crossrefs

Cf. A005117, A381639, A381640, A381641.

Programs

Mathematica

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]

PARI

f(n) = {my(p = factor(n)[,1]); sum(i = 1, #p-1, 1 - p[i]/p[i+1]);}
list(lim) = {my(fm = -1, f1); for(k = 1, lim, f1 = f(k); if(f1 > fm, print1(k, ", "); fm = f1));}