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A103635 Positions of running maxima of log(g(n))/sqrt(n*log(n)), where g(n) is Landau's function A000793. 1
2, 3, 5, 7, 9, 10, 12, 17, 19, 30, 36, 40, 43, 47, 49, 53, 60, 64, 66, 70, 83, 85, 89, 108, 112, 141, 172, 209, 250, 258, 293, 301, 321, 340, 348, 360, 368, 401, 413, 421, 480, 533, 541, 608, 626, 679, 697, 752, 770, 831, 849, 914, 932, 1021, 1118, 1160, 1219 (list; graph; refs; listen; history; text; internal format)
OFFSET
2,1
COMMENTS
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
LINKS
Amiram Eldar, Table of n, a(n) for n = 2..378 (calculated using the MAPLE code by Deléglise et al.; terms 2..123 from Alois P. Heinz)
Marc Deléglise, Jean-Louis Nicolas, and Paul Zimmermann, Landau's function for one million billions, Journal de Théorie des Nombres de Bordeaux, Vol. 20, No. 3 (2008), pp. 625-671.
Marc Deléglise, Jean-Louis Nicolas, and Paul Zimmermann, Computation of the Landau function g(n) (MAPLE code).
Jean-Pierre Massias, Majoration explicite de l'ordre maximum d'un élément du groupe symétrique, Annales de la Faculté des sciences de Toulouse: Mathématiques, Vol. 6, No. 3-4 (1984), pp. 269-281.
Eric Weisstein's World of Mathematics, Landau's Function
EXAMPLE
From Jon E. Schoenfield, Aug 16 2015: (Start)
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)):
n g(n) log(g(n))/sqrt(n*log(n))
== ==== ========================
1 1 (undefined)
a(1) = 2 2 0.588705 <--- record high
a(2) = 3 3 0.605148 <--- record high
4 4 0.588705
a(3) = 5 6 0.631623 <--- record high
6 6 0.546467
a(4) = 7 12 0.673286 <--- record high
8 15 0.663955
a(5) = 9 20 0.673666 <--- record high
a(6) = 10 30 0.708800 <--- record high
(End)
MATHEMATICA
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 *)
CROSSREFS
Cf. A000793.
Sequence in context: A047371 A327492 A044918 * A133677 A362403 A075750
KEYWORD
nonn,fini,full
AUTHOR
Eric W. Weisstein, Feb 11 2005
EXTENSIONS
More terms from R. J. Mathar, Feb 14 2008
More terms from Alois P. Heinz, Feb 18 2013
STATUS
approved

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Last modified July 22 06:32 EDT 2024. Contains 374481 sequences. (Running on oeis4.)