A096123 Least product n*(n-1)*(n-2)*...*(n-k+1) divisible by (n-k)!.

1, 2, 6, 12, 60, 120, 840, 1680, 15120, 5040, 55440, 665280, 8648640, 17297280, 259459200, 518918400, 8821612800, 17643225600, 335221286400, 670442572800, 14079294028800, 28158588057600, 647647525324800, 1295295050649600

Offset: 1

Author

Amarnath Murthy, Jul 01 2004

Keywords

• nonn

Comments

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.

Examples

			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.
		

Crossrefs

Cf. A056042, A096974.

Programs

PARI

{for(n=1,24,p=1;k=0;b=1;while(b&&k
				

Extensions

Edited and extended by Klaus Brockhaus, Jul 17 2004