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%I #29 Aug 23 2019 17:27:54
%S 2,3,5,7,9,10,12,17,19,30,36,40,43,47,49,53,60,64,66,70,83,85,89,108,
%T 112,141,172,209,250,258,293,301,321,340,348,360,368,401,413,421,480,
%U 533,541,608,626,679,697,752,770,831,849,914,932,1021,1118,1160,1219
%N Positions of running maxima of log(g(n))/sqrt(n*log(n)), where g(n) is Landau's function A000793.
%C Massias proved that the function log(g(n))/sqrt(n*log(n)) reaches its maximum at n = 1319766. Therefore this sequence is finite, with a(378) = 1319766 being the last term. - _Amiram Eldar_, Aug 23 2019
%H Amiram Eldar, <a href="/A103635/b103635.txt">Table of n, a(n) for n = 2..378</a> (calculated using the MAPLE code by Deléglise et al.; terms 2..123 from Alois P. Heinz)
%H Marc Deléglise, Jean-Louis Nicolas, and Paul Zimmermann, <a href="http://archive.numdam.org/item/JTNB_2008__20_3_625_0/">Landau's function for one million billions</a>, Journal de Théorie des Nombres de Bordeaux, Vol. 20, No. 3 (2008), pp. 625-671.
%H Marc Deléglise, Jean-Louis Nicolas, and Paul Zimmermann, <a href="http://math.univ-lyon1.fr/homes-www/nicolas/landaug.html">Computation of the Landau function g(n)</a> (MAPLE code).
%H Jean-Pierre Massias, <a href="https://eudml.org/doc/73167">Majoration explicite de l'ordre maximum d'un élément du groupe symétrique</a>, Annales de la Faculté des sciences de Toulouse: Mathématiques, Vol. 6, No. 3-4 (1984), pp. 269-281.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/LandausFunction.html">Landau's Function</a>
%e From _Jon E. Schoenfield_, Aug 16 2015: (Start)
%e Terms are the values of n at which record high values of the ratio log(g(n))/sqrt(n*log(n)) occur (where g(n) = A000793(n)):
%e n g(n) log(g(n))/sqrt(n*log(n))
%e == ==== ========================
%e 1 1 (undefined)
%e a(1) = 2 2 0.588705 <--- record high
%e a(2) = 3 3 0.605148 <--- record high
%e 4 4 0.588705
%e a(3) = 5 6 0.631623 <--- record high
%e 6 6 0.546467
%e a(4) = 7 12 0.673286 <--- record high
%e 8 15 0.663955
%e a(5) = 9 20 0.673666 <--- record high
%e a(6) = 10 30 0.708800 <--- record high
%e (End)
%t g[n_] := Max@Apply[LCM, IntegerPartitions@n, 1]; f[n_] := Log[g[n]]/Sqrt[n * Log[n]]; fm = 0; s = {}; Do[f1 = f[n]; If[f1 > fm, fm = f1; AppendTo[s, n]], {n, 2, 100}]; s (* _Amiram Eldar_, Aug 23 2019 after _Robert G. Wilson v_ at A000793 *)
%Y Cf. A000793.
%K nonn,fini,full
%O 2,1
%A _Eric W. Weisstein_, Feb 11 2005
%E More terms from _R. J. Mathar_, Feb 14 2008
%E More terms from _Alois P. Heinz_, Feb 18 2013
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