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A095996
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a(n) = largest divisor of n! that is coprime to n.
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8
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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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Vincenzo Librandi, Table of n, a(n) for n = 1..200
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FORMULA
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a(p) = (p-1)!.
a(n) = n!/A051696(n) = (n-1)!/A062763(n).
a(n) = numerator(Sum_{j = 0..n} (-1)^(n-j)*binomial(n,j)*(j/n+1)^n ). - Vladimir Kruchinin, Jun 02 2013
a(n) = denominator(n^n/n!). - Vincenzo Librandi Sep 04 2014
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MAPLE
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series(LambertW(x), x, 30); # N. J. A. Sloane, Jan 08 2021
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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 *)
Table[Denominator[n^n/n!], {n, 30}] (* Vincenzo Librandi, Sep 04 2014 *)
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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);
makelist(num(a(n), n, 1, 20); /* Vladimir Kruchinin, Jun 02 2013 */
(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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Cf. A036503, A227831, A066570.
Sequence in context: A329456 A037277 A001783 * A308943 A061098 A160630
Adjacent sequences: A095993 A095994 A095995 * A095997 A095998 A095999
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KEYWORD
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nonn
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AUTHOR
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Robert G. Wilson v, Jul 19 2004, based on a suggestion from Leroy Quet, Jun 18 2004
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STATUS
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approved
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