A096127 -id:A096127 - cp's OEIS frontend

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

Amarnath Murthy, Jul 03 2004

nonn

(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.

			a(4) = 16!/(4!)^5 = 2627625 which is not further divisible by 24.

Andrew Howroyd, Table of n, a(n) for n = 1..25

Cf. A034841, A057599, A096127.

a(n)={if(n==1, 1, (n^2)!/(n!^valuation((n^2)!,n!)))} \\ Andrew Howroyd, Nov 09 2019

Edited by Don Reble, Jul 04 2004

a(9) from Andrew Howroyd, Nov 09 2019

A244443 Smallest integer m > 1 such that m!^(m + n) divides (m^2)!.

Original entry on oeis.org

2, 6, 15, 77, 185, 187, 475, 3820, 4043, 4090, 11231, 30589, 57023, 126815, 131055, 983032, 983033, 2617339, 4046839, 11534206, 11534207, 65011702, 66777087, 368279551, 469745405, 973061887, 1064828671

Offset: 1

Farideh Firoozbakht, Aug 24 2014

The constraint m > 1 is necessary because (1^2)! = 1.
The motivation for this sequence came from comments on the sequence A246048 by M. F. Hasler.
The integer (3820^2)!/(3820!)^3828 related to a(8) has 52166326 digits, so it isn't easy to find more terms.
a(28) > 1.5 * 10^9. - Hiroaki Yamanouchi, Sep 29 2014

			a(4) = 77 because 77!^(77 + 4) divides (77^2)! and 77 is the smallest integer m, m > 1, with this property.

Cf. A096126, A096127, A246048.

for(n=1, 7, m=2; while((m^2)!%(m!^(m+n)), m++); print1(m", ")) \\ Jens Kruse Andersen, Aug 31 2014

n=f=1; for(m=2, 5000, f*=m; s=m^2; forprime(p=2, m, e=0; b=p; while(b<=s, e+=s\b; b*=p); if(valuation(f,p)*(m+n)>e, next(2))); print1(m", "); n++) \\ Faster program. Jens Kruse Andersen, Aug 31 2014

a(9)-a(13) from Jens Kruse Andersen, Aug 31 2014

a(14)-a(27) from Hiroaki Yamanouchi, Sep 29 2014

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

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A244443 Smallest integer m > 1 such that m!^(m + n) divides (m^2)!.

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Author

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Comments

Examples

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Programs

PARI

PARI

Extensions