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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 (list; graph; refs; listen; history; text; internal format)
 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 Andrew Howroyd, Table of n, a(n) for n = 1..25 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 Cf. A034841, A057599, A096127. Sequence in context: A003706 A068250 A263884 * A057599 A239273 A054583 Adjacent sequences:  A096123 A096124 A096125 * A096127 A096128 A096129 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

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Last modified December 8 09:32 EST 2019. Contains 329862 sequences. (Running on oeis4.)