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

1,2

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.

Links

Table of n, a(n) for n=1..24.

Example

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.

Prog

(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++)))}

Crossrefs

Cf. A056042, A096974.

Sequence in context: A185021 A191836 A072486 * A081125 A138570 A161887

Adjacent sequences: A096120 A096121 A096122 * A096124 A096125 A096126

Keyword

nonn

Author

Amarnath Murthy, Jul 01 2004

Extensions

Edited and extended by Klaus Brockhaus, Jul 17 2004

Status

approved