login
This site is supported by donations to The OEIS Foundation.

 

Logo

Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing.
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

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