0,3

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

Grantham mentions that he computed a(n) for n <= 500000.

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.

J. Kuzmanovich and A. Pavlichenkov, Finite groups of matrices whose entries are integers, Amer. Math. Monthly, 109 (2002), 173-186.

W. Miller, The Maximum Order of an Element of Finite Symmetric Group, Am. Math. Monthly, Jun-Jul 1987, pp. 497-506.

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.

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.

J.-L. Nicolas, On Landau's function g(n), pp. 228-240 of R. L. Graham et al., eds., Mathematics of Paul Erdos I.

David Wasserman, Table of n, a(n) for n = 0..814

Jon Grantham, The largest prime dividing the maximal order of an element of S_n, Math. Comput. 64, No. 209, 407-410 (1995).

J.-L. Nicolas, Sur l'ordre maximum d'un element dans le groupe Sn des permutations, Acta Arith. 14, 315-332 (1968).

J.-L. Nicolas, Ordre maximal d'un element du groupe S_n des permutations et 'highly composite numbers', Bull. Soc. Math. France 97 (1969), 129-191.

Eric Weisstein's World of Mathematics, Landau's Function

Index entries for sequences related to lcm's

Index entries for "core" sequences

Landau: lim_{n->infinity} (log a(n)) / sqrt(n log n) = 1.

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

seq( max( op( map( x->ilcm(op(x)), combinat[partition](n)))), n=1..30); - David G. Radcliffe (radcl008(AT)umn.edu), Feb 28 2006

Table[ Max[ Union[ Apply[ LCM, Partitions[ n ], 1 ] ] ], {n, 30} ]

(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 */

Cf. A000792, A009490, A034891, A074859.

Adjacent sequences: A000790 A000791 A000792 this_sequence A000794 A000795 A000796

Sequence in context: A007464 A064764 A123131 this_sequence A062163 A002729 A030209

nonn,core,easy,nice

njas

More terms from David W. Wilson (davidwwilson(AT)comcast.net).