

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 nth antidiagonal.


1



1, 4, 18, 576, 1200, 518400, 1587600, 180633600, 1646023680, 13168189440000, 461039040000, 229442532802560000, 86553098311680000, 3753113311877529600, 834966920275488000000
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,2


COMMENTS

If n is even and n+1 is prime, a(n) = n^2 * (n1)!^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*(n1)*((n1)/2)!. This was proved by Lawrence Sze.  Ralf Stephan, Nov 16 2004


LINKS



FORMULA

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


EXAMPLE

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 nth row.


PROG

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


CROSSREFS



KEYWORD

nonn


AUTHOR



EXTENSIONS



STATUS

approved



