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A096126
a(n) is the least integer of the form (n^2)!/(n!)^k.
5
1, 3, 280, 2627625, 5194672859376, 5150805819130303332, 1461034854396267778567973305958400, 450538787986875167583433232345723106006796340625, 146413934927214422927834111686633731590253260933067148964500000000
OFFSET
1,2
COMMENTS
(n^2)!/(n!)^(n+1) is an integer for every n (see A057599). Hence k >= n+1. Conjecture: k=n+1 only when n is prime or a power of a prime.
LINKS
EXAMPLE
a(4) = 16!/(4!)^5 = 2627625 which is not further divisible by 24.
PROG
(PARI) a(n)={if(n==1, 1, (n^2)!/(n!^valuation((n^2)!, n!)))} \\ Andrew Howroyd, Nov 09 2019
CROSSREFS
KEYWORD
nonn
AUTHOR
Amarnath Murthy, Jul 03 2004
EXTENSIONS
Edited by Don Reble, Jul 04 2004
a(9) from Andrew Howroyd, Nov 09 2019
STATUS
approved