A096126 a(n) is the least integer of the form (n^2)!/(n!)^k.

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

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: A068250 A364617 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