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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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10
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1, 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
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OFFSET
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0,4
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REFERENCES
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J.-L. Nicolas, On Landau's function g(n), pp. 228-240 of R. L. Graham et al., eds., Mathematics of Paul Erdős I.
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LINKS
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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, Sep 29 2002
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MATHEMATICA
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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}] (* Jean-François Alcover, Nov 03 2011, after Vladeta Jovovic *)
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CROSSREFS
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Cf. A000793 (Landau's function g(n)).
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KEYWORD
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easy,nice,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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