%I #17 Aug 18 2014 08:10:17
%S 1,2,3,8,12,24,40,60,144,240,360,720,1008,1680,2520,5760,8064,13440,
%T 20160,51840,72576,120960,181440,518400,725760,1209600,1814400,
%U 3628800,5702400,7983360,13305600,19958400,43545600,68428800,95800320,159667200,239500800,479001600,566092800
%N Numbers n such that k!/n is prime for some k.
%C This sequence is the union of the sequences {n!/p: p | n! and p is prime}. Thus this sequence is infinite.
%H Jens Kruse Andersen, <a href="/A242516/b242516.txt">Table of n, a(n) for n = 1..1000</a>
%o (PARI)
%o a(n)=for(k=1,n+2,s=k!/n;if(floor(s)==s,if(ispseudoprime(s),return(k))))
%o n=1;while(n<10000,if(a(n),print1(n,", "));n++)
%o (PARI)
%o v=[];for(n=1,50,forprime(p=1,n,v=concat(v,n!/p)));vecsort(v) \\ faster program
%Y Cf. A242457.
%K nonn
%O 1,2
%A _Derek Orr_, Aug 16 2014