A109914 Product of all composite numbers k such that n! < k < prime(r) where prime(r-1)< n!.

1, 1, 1, 491400, 3546112878000, 143424700959632400, 10691567972893973348743970911396896000, 210948344078434820704169472200928966427054605885088717074131707385374604732966434908020301638860800000

Offset: 1

Author

Amarnath Murthy, Jul 16 2005

Keywords

• nonn

Comments

k divides n!.

If n is in A002981, then a(n) is - by definition - 1. If not, then none of the numbers n!+1, n!+2, ... n!+n will be prime, which gives us the lower bound a(n) > (n!+1)^n. - Stefan Steinerberger, Mar 14 2006

Examples

			a(4) = 25*26*27*28 =491400.
		

Crossrefs

Cf. A109915.

Programs

Mathematica

Table[Product[i, {i, n! + 1, Prime[PrimePi[n! ] + 1] - 1}], {n, 1, 8}] (* Stefan Steinerberger, Mar 14 2006 *)

Extensions

More terms from Stefan Steinerberger, Mar 14 2006