Grids Of Coprime Rows, Columns, (Diagonals)

[Leroy Quet]

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