A068819 n!/((n+1)*(n+2)*...*(n+k)) where k is largest value that gives an integer quotient.

1, 2, 6, 24, 20, 720, 7, 448, 36288, 3628800, 3326400, 479001600, 1853280, 363242880, 81729648000, 20922789888000, 19760412672000, 6402373705728000, 13165054156800, 5266021662720000, 2322315553259520000

Offset

1,2

Comments

n! is divisible by all the numbers from n+1 to n+k where n+k+1 is the smallest prime greater than n. Conjecture: For n > 3 n! is divisible by product(n+k,n)= (n+1)(n+2)...(n+k).

References

Amarnath Murthy, Smarandache Reciprocal function and an elementary inequality. Smarandache Notions Journal Vol. 11, 2000.

Links

T. D. Noe, Table of n, a(n) for n = 1..200

Formula

a(n) = smallest integer value of (n!)^2/(n+k)! i.e. n+k+1 does not divide a(n).

Example

a(7)= 7 as 5040/8 = 630, 630/9 = 70, 70/10 = 7 but 7 is not divisible by 11.

Mathematica

a[3] = 6; a[n_] := n!^2/(NextPrime[n]-1)!; Table[a[n], {n, 1, 21}](* Jean-François Alcover, Feb 16 2012 *)

Crossrefs

Sequence in context: A319544 A354833 A124900 * A060068 A099732 A118381

Adjacent sequences: A068816 A068817 A068818 * A068820 A068821 A068822

Keyword

easy,nice,nonn

Author

Amarnath Murthy, Mar 08 2002

Extensions

Corrected by T. D. Noe, May 08 2007

Status

approved