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
KEYWORD
easy,nice,nonn
AUTHOR
Amarnath Murthy, Mar 08 2002
EXTENSIONS
Corrected by T. D. Noe, May 08 2007
STATUS
approved