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Search: id:A074859
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| A074859 |
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Number of elements of S_n having the maximum possible order g(n), where g(n) is Landau's function (A000793). |
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7
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| 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; listen)
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OFFSET
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1,3
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REFERENCES
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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.
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FORMULA
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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
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CROSSREFS
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Cf. A000793 (Landau's function g(n)).
Cf. A074064, A074103, A074115.
Sequence in context: A156334 A082690 A104861 this_sequence A162682 A103160 A126099
Adjacent sequences: A074856 A074857 A074858 this_sequence A074860 A074861 A074862
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KEYWORD
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easy,nice,nonn
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AUTHOR
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Chris Smyth (chris(AT)maths.ed.ac.uk), Sep 11 2002
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EXTENSIONS
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Corrected and extended by Vladeta Jovovic (vladeta(AT)eunet.rs), Sep 20 2002
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