%I A096123
%S A096123 1,2,6,12,60,120,840,1680,15120,5040,55440,665280,8648640,17297280,
%T A096123 259459200,518918400,8821612800,17643225600,335221286400,670442572800,
%U A096123 14079294028800,28158588057600,647647525324800,1295295050649600
%N A096123 Least product n*(n-1)*(n-2)*...*(n-k+1) divisible by (n-k)!.
%C A096123 Conjecture: a(n) = n!/(p-1)! for all sufficiently large n, where p is 
               the least prime such that n <= 2*p (Amarnath Murthy). A096974 gives 
               numbers n such that a(n) = n!/(nextprime(n/2)-1)! and indicates that 
               this conjecture is most probably false.
%e A096123 a(10) = 5040 as 10*9 is not divisible by 8!, 10*9*8 is not divisible 
               by 7! but 10*9*8*7 = 5040 is divisible by 6! = 720.
%o A096123 (PARI) {for(n=1,24,p=1;k=0;b=1;while(b&&k<n,p=p*(n-k);d=(n-k)!;if(p%d==0,
               b=0;print1(p,","),k++)))}
%Y A096123 Cf. A056042, A096974.
%Y A096123 Sequence in context: A004490 A135060 A072486 this_sequence A081125 A138570 
               A161887
%Y A096123 Adjacent sequences: A096120 A096121 A096122 this_sequence A096124 A096125 
               A096126
%K A096123 nonn
%O A096123 1,2
%A A096123 Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Jul 01 2004
%E A096123 Edited and extended by Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), 
               Jul 17 2004