A082022 In the following square array a(i,j) = Least Common Multiple of i and j. Sequence contains the product of the terms of the n-th antidiagonal.

1, 4, 18, 576, 1200, 518400, 1587600, 180633600, 1646023680, 13168189440000, 461039040000, 229442532802560000, 86553098311680000, 3753113311877529600, 834966920275488000000

Offset: 1

Author

Amarnath Murthy, Apr 06 2003

Keywords

• nonn

Comments

If n is even and n+1 is prime, a(n) = n^2 * (n-1)!^2. If n is odd and >3, 2*(n+1)*a(n) is a perfect square, the root of which has the factor 1/2*n*(n-1)*((n-1)/2)!. This was proved by Lawrence Sze. - Ralf Stephan, Nov 16 2004

Examples

			1 2 3 4 5...
2 2 6 4 10...
3 6 3 12 15...
4 4 12 4 20...
5 10 15 20 5...
...
The same array in triangular form is
1
2 2
3 2 3
4 6 6 4
5 4 3 4 5
...
Sequence contains the product of the terms of the n-th row.
		

Crossrefs

Cf. A006580, A003990, A082292.

Equals A001044(n) / A051190(n+1).

Programs

PARI

for(n=1,20,p=1:for(k=1,n,p=p*lcm(k,n+1-k)):print1(p","))

Formula

Prod(k=1...n, lcm(k, n+1-k)).

Extensions

Corrected and extended by Ralf Stephan, Apr 08 2003