Search: id:A000793
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%I A000793 M0537 N0190
%S A000793 1,1,2,3,4,6,6,12,15,20,30,30,60,60,84,105,140,210,210,420,420,420,420,
%T A000793 840,840,1260,1260,1540,2310,2520,4620,4620,5460,5460,9240,9240,13860,
%U A000793 13860,16380,16380,27720,30030,32760,60060,60060,60060,60060,120120
%N A000793 Landau's function g(n): largest order of permutation of n elements. Equivalently, 
               largest lcm of partitions of n.
%C A000793 Also the largest orbit size (cycle length) for the permutation A057511 
               acting on Catalan objects (e.g. planar rooted trees, parenthesizations) 
               - Antti Karttunen Sep 07 2000
%C A000793 Grantham mentions that he computed a(n) for n <= 500000.
%D A000793 J. Haack, "The Mathematics of Steve Reich's Clapping Music," in Bridges: 
               Mathematical Connections in Art, Music and Science: Conference Proceedings, 
               1998, Reza Sarhangi (ed.), 87-92.
%D A000793 J. Kuzmanovich and A. Pavlichenkov, Finite groups of matrices whose entries 
               are integers, Amer. Math. Monthly, 109 (2002), 173-186.
%D A000793 Edmund Georg Hermann Landau, Handbuch der Lehre von der Verteilung der 
               Primzahlen, Chelsea Publishing, NY 1953, p. 223.
%D A000793 W. Miller, The Maximum Order of an Element of Finite Symmetric Group, 
               Am. Math. Monthly, Jun-Jul 1987, pp. 497-506.
%D A000793 J.-L. Nicolas, Sur l'ordre maximum d'un e'le'ment dans le groupe S_n 
               des permutations, Acta Arith., 14 (1968), 315-332.
%D A000793 J.-L. Nicolas, Ordre maximum d'un e'le'ment du groupe de permutations 
               et highly composite numbers, Bull. Math. Soc. France, 97 (1969), 
               129-191.
%D A000793 J.-L. Nicolas, On Landau's function g(n), pp. 228-240 of R. L. Graham 
               et al., eds., Mathematics of Paul Erdos I.
%D A000793 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A000793 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%H A000793 David Wasserman, <a href="b000793.txt">Table of n, a(n) for n = 0..814</
               a>
%H A000793 Jon Grantham, <a href="http://www.pseudoprime.com/landau.ps">The largest 
               prime dividing the maximal order of an element of S_n</a>, Math. 
               Comput. 64, No. 209, 407-410 (1995).
%H A000793 J.-L. Nicolas, <a href="http://matwbn.icm.edu.pl/ksiazki/aa/aa14/aa1420.pdf">
               Sur l'ordre maximum d'un element dans le groupe Sn des permutations</
               a>, Acta Arith. 14, 315-332 (1968).
%H A000793 J.-L. Nicolas, <a href="http://archive.numdam.org/article/BSMF_1969__97__129_0.pdf">
               Ordre maximal d'un element du groupe S_n des permutations et 'highly 
               composite numbers'</a>, Bull. Soc. Math. France 97 (1969), 129-191.
%H A000793 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               LandausFunction.html">Landau's Function</a>
%H A000793 <a href="Sindx_Lc.html#lcm">Index entries for sequences related to lcm's</
               a>
%H A000793 <a href="Sindx_Cor.html#core">Index entries for "core" sequences</a>
%F A000793 Landau: lim_{n->infinity} (log a(n)) / sqrt(n log n) = 1.
%p A000793 with(combinat): for n from 0 to 30 do l := 1: p := partition(n): for 
               i from 1 to numbpart(n) do if ilcm( p[i][j] $ j=1..nops(p[i])) > 
               l then l := ilcm( p[i][j] $ j=1..nops(p[i])) fi: od: printf(`%d,`,
               l): od: # from James A. Sellers Dec 07 2000
%p A000793 seq( max( op( map( x->ilcm(op(x)), combinat[partition](n)))), n=1..30); 
               - David G. Radcliffe (radcl008(AT)umn.edu), Feb 28 2006
%t A000793 Table[ Max[ Union[ Apply[ LCM, Partitions[ n ], 1 ] ] ], {n, 30} ]
%o A000793 (PARI) a(n)=local(m,t,j,u);if(n<2,n>=0, m=ceil(n/exp(1)); t=ceil((n/m)^m); 
               j=1; for(i=2,t, u=factor(i); u=sum(k=1,matsize(u)[1],u[k,1]^u[k,2]); 
               if(u<=n, j=i));j) /* Michael Somos Oct 20 2004 */
%Y A000793 Cf. A000792, A009490, A034891, A074859.
%Y A000793 Sequence in context: A007464 A064764 A123131 this_sequence A062163 A002729 
               A030209
%Y A000793 Adjacent sequences: A000790 A000791 A000792 this_sequence A000794 A000795 
               A000796
%K A000793 nonn,core,easy,nice
%O A000793 0,3
%A A000793 N. J. A. Sloane (njas(AT)research.att.com).
%E A000793 More terms from David W. Wilson (davidwwilson(AT)comcast.net).
%E A000793 Removed erroneous comment about a(16) which probably originated from 
               misreading a(15)=105 as a(16) because of offset=0: a(16)=4*5*7=140 
               is correct as it stands. - M. F. Hasler (MHasler(AT)univ-ag.fr), 
               Feb 02 2009

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