Formula to generate dense non-random non-singular matrix?

Question

Mathematics

For a given dimension n, a nonsingular matrix must be generated.
I would like some simple formula like a(i,j)=1/(i + j). But most of these simple formulas give degenerate matrices.
Why?
There is a known method of generating based on a list of prime numbers ( See ).
What other options are there?

PS
We came up with the following options (octave, matlab): More? PPS An example where a(i,j) is an analytic function?
i = [1:n]'; j = [1:n]; a = rem(i, j+1)
i = [1:n]'; j = [1:n]; a = idivide(i, j)

Answer 1

a = ( i == j ? 1 : 0 )
another option:
a = ( i >= j ? 1 : 0 )
third option:
a = ( i <= j ? 1 : 0 )
fourth option:
a = ( i = = n+1-j ? 1 : 0 )
fifth option:
a = ( i >= n+1-j ? 1 : 0 )
sixth option:
a = ( i <= n+1-j ? 1 : 0 )