OFFSET
1,1
COMMENTS
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
Paul Erdős and Ilias Kastanas, Solution 6674: The smallest factorial that is a multiple of n, Amer. Math. Monthly, Vol. 101, No. 2 (1994), p. 179.
Aubrey J. Kempner, Miscellanea, Amer. Math. Monthly, Vol. 25, No. 5 (1918), pp. 201-210. See Section II, "Concerning the smallest integer m! divisible by a given integer n."
Eric Weisstein's World of Mathematics, Greatest Prime Factor.
EXAMPLE
12 does not divide P(12)! = 3! and 3^2 is not a factor of 12.
MATHEMATICA
q[n_] := Module[{p = FactorInteger[n][[-1, 1]]}, !Divisible[n, p^2] && !Divisible[p!, n]]; Select[Range[1500], q] (* Amiram Eldar, Mar 30 2021 *)
PROG
(PARI) isok(n) = {my(f = factor(n)); my(P = f[#f~, 1]); (P! % n) && (n % P^2); } \\ Michel Marcus, Sep 16 2015
CROSSREFS
KEYWORD
nonn
AUTHOR
Jonathan Sondow, Dec 28 2004
EXTENSIONS
More terms from Michel Marcus, Sep 16 2015
STATUS
approved