Grids Of Coprime Rows, Columns, (Diagonals)

[David Wasserman]

Dear Leroy,

I would want to solve the simplest version of the problem before I would try it in the form you posted.  To make it simpler, I would eliminate the diagonal requirement and the adjacency requirement.  Has this problem already been solved?  It might turn out to be equal to some familiar sequence.  

To make it even simpler, eliminate the restriction that all of the numbers have to be distinct.  For example,
1 2
2 1

1 2 3
2 3 1
3 1 2

1 2 3 5
2 3 5 1
3 5 1 2
5 1 2 3
But that makes it too simple; the resulting sequence is just 1 followed by the primes.

>I posted the following puzzle to sci.math and rec.puzzles:
>http://groups.google.com/groups?hl=en&lr=&ie=UTF-8&threadm=cntgv4%249j8%241
>%40newslocal.mitre.org&prev=
>
>My reason for posting this email to seq.fan is that I wonder,
>what is the sequence of lowest possible integers when n=1,2,3,...?
>
>For example, a(4) = 23.
>
>And another sequence might be,
>what if we allow non-coprime integers in the diagonals (we concern 
>ourselves only with the rows and columns)?
>
>thanks,
>Leroy Quet