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A068819
n!/((n+1)*(n+2)*...*(n+k)) where k is largest value that gives an integer quotient.
1
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.
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
KEYWORD
easy,nice,nonn
AUTHOR
Amarnath Murthy, Mar 08 2002
EXTENSIONS
Corrected by T. D. Noe, May 08 2007
STATUS
approved