|
| |
|
|
A074859
|
|
Number of elements of S_n having the maximum possible order g(n), where g(n) is Landau's function (A000793).
|
|
6
| |
|
|
1, 1, 2, 6, 20, 240, 420, 2688, 18144, 120960, 2661120, 7983360, 103783680, 1037836800, 12454041600, 149448499200, 1693749657600, 60974987673600, 289631191449600, 5792623828992000, 121645100408832000, 3568256278659072000, 30776210403434496000, 738629049682427904000, 12310484161373798400000
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 1,3
|
|
|
REFERENCES
| 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.
|
|
|
FORMULA
| a(n) = n!*coefficient of x^n in expansion of Sum_{i divides A000793(n)} mu(A000793(n)/i)*exp(Sum_{j divides i} x^j/j). - Vladeta Jovovic (vladeta(AT)eunet.rs), Sep 29 2002
|
|
|
MATHEMATICA
| g[n_] := Max[ Apply[ LCM, IntegerPartitions[n], 1]]; f[x_, n_] := Total[ (MoebiusMu[g[n]/#]*Exp[ Total[ (x^#/# & ) /@ Divisors[#]]] & ) /@ Divisors[g[n]]]; a[n_] := n!*Coefficient[ Series[f[x, n], {x, 0, n}], x^n]; Table[a[n], {n, 1, 25}] (* From Jean-François Alcover, Nov 03 2011, after Vladeta Jovovic *)
|
|
|
CROSSREFS
| Cf. A000793 (Landau's function g(n)).
Cf. A074064, A074103, A074115.
Sequence in context: A156334 A082690 A104861 * A162682 A103160 A126099
Adjacent sequences: A074856 A074857 A074858 * A074860 A074861 A074862
|
|
|
KEYWORD
| easy,nice,nonn
|
|
|
AUTHOR
| Chris Smyth (chris(AT)maths.ed.ac.uk), Sep 11 2002
|
|
|
EXTENSIONS
| Corrected and extended by Vladeta Jovovic (vladeta(AT)eunet.rs), Sep 20 2002
|
| |
|
|
