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A095996 a(n) = largest divisor of n! that is coprime to n. 8
1, 1, 2, 3, 24, 5, 720, 315, 4480, 567, 3628800, 1925, 479001600, 868725, 14350336, 638512875, 20922789888000, 14889875, 6402373705728000, 14849255421, 7567605760000, 17717861581875, 1124000727777607680000, 2505147019375 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

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

REFERENCES

R. L. Graham, D. E. Knuth and O. Patashnik, Concrete Mathematics, Addison-Wesley, 2nd ed., Eq. (5.66).

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..200

FORMULA

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

MAPLE

series(LambertW(x), x, 30); # N. J. A. Sloane, Jan 08 2021

MATHEMATICA

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 *)

PROG

(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

CROSSREFS

Cf. A036503, A227831, A066570.

Sequence in context: A329456 A037277 A001783 * A308943 A061098 A160630

Adjacent sequences:  A095993 A095994 A095995 * A095997 A095998 A095999

KEYWORD

nonn

AUTHOR

Robert G. Wilson v, Jul 19 2004, based on a suggestion from Leroy Quet, Jun 18 2004

STATUS

approved

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Last modified March 7 18:28 EST 2021. Contains 341909 sequences. (Running on oeis4.)