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A058067 Number of polynomial functions from Z to Z/nZ. 3
1, 1, 4, 27, 64, 3125, 108, 823543, 1024, 19683, 12500, 285311670611, 1728, 302875106592253, 3294172, 84375, 65536, 827240261886336764177, 78732, 1978419655660313589123979, 200000, 22235661, 1141246682444, 20880467999847912034355032910567 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

The first formula for a(n) is due to Kempner (1921). - Jonathan Sondow, Nov 05 2017

LINKS

Table of n, a(n) for n=0..23.

M. Bhargava, The factorial function and generalizations, Amer. Math. Monthly, 107 (Nov. 2000), 783-799.

A. J. Kempner, Polynomials and their residue systems, continued, Amer. Math. Soc. Trans., 22 (1921), 240-288.

FORMULA

a(n) = Product_{k=0..n-1} n/gcd(n, k!).

Multiplicative with a(p^e) = p^t_p(e). - David W. Wilson, Aug 14 2005 [t_p(e) = Sum_{k>=0: e > A090622(k, p)} (e - A090622(k, p)). - Andrey Zabolotskiy, Nov 09 2017]

a(prime(n)) = A051674(n). - R. J. Mathar, Apr 01 2014 [Edited by Andrey Zabolotskiy, Nov 08 2017]

a(n) = n^n / A240098(n). - Jonathan Sondow, Nov 10 2017

MAPLE

A058067 := n->mul(n/gcd(n, k!), k=0..n-1);

PROG

(PARI) a(n) = prod(k=0, n-1, n/gcd(n, k!)); \\ Michel Marcus, Nov 06 2017

CROSSREFS

Cf. A051674, A090622, A240098.

Sequence in context: A186882 A097792 A308474 * A294038 A175701 A227866

Adjacent sequences:  A058064 A058065 A058066 * A058068 A058069 A058070

KEYWORD

nonn,mult

AUTHOR

N. J. A. Sloane, Nov 24 2000

STATUS

approved

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Last modified August 25 13:50 EDT 2019. Contains 326324 sequences. (Running on oeis4.)