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.

Edmund Georg Hermann Landau, Handbuch der Lehre von der Verteilung der Primzahlen, Chelsea Publishing, NY 1953, p. 223.

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.

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

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

N. J. A. Sloane (njas(AT)research.att.com).

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

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