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A095996
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a(n) = largest divisor of n! that is coprime to n.
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9
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1, 1, 2, 3, 24, 5, 720, 315, 4480, 567, 3628800, 1925, 479001600, 868725, 14350336, 638512875, 20922789888000, 14889875, 6402373705728000, 14849255421, 7567605760000, 17717861581875, 1124000727777607680000, 2505147019375
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OFFSET
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1,3
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COMMENTS
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The denominators of the coefficients in Taylor series for LambertW(x) are 1, 1, 1, 2, 3, 24, 5, 720, 315, 4480, 567, 3628800, 1925, ..., which is this sequence prefixed by 1. (Cf. A227831.) - N. J. A. Sloane, Aug 02 2013
The second Mathematica program is faster than the first for large n. - T. D. Noe, Sep 07 2013
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REFERENCES
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R. L. Graham, D. E. Knuth and O. Patashnik, Concrete Mathematics, Addison-Wesley, 2nd ed., Eq. (5.66).
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LINKS
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FORMULA
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a(p) = (p-1)!.
a(n) = numerator(Sum_{j = 0..n} (-1)^(n-j)*binomial(n,j)*(j/n+1)^n ). - Vladimir Kruchinin, Jun 02 2013
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MAPLE
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MATHEMATICA
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f[n_] := Select[Divisors[n! ], GCD[ #, n] == 1 &][[ -1]]; Table[f[n], {n, 30}]
Denominator[Exp[Table[Limit[Zeta[s]*Sum[(1 - If[Mod[k, n] == 0, n, 0])/k^(s - 1), {k, 1, n}], s -> 1], {n, 1, 30}]]] (* Conjecture Mats Granvik, Sep 09 2013 *)
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PROG
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(Maxima)
a(n):=sum((-1)^(n-j)*binomial(n, j)*(j/n+1)^n, j, 0, n);
(Magma) [Denominator(n^n/Factorial(n)): n in [1..25]]; // Vincenzo Librandi, Sep 04 2014
(PARI) for(n=1, 50, print1(denominator(n^n/n!), ", ")) \\ G. C. Greubel, Nov 14 2017
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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