To produce all pairs (the catesian product) fom two enumerations, we need
a version of Cantor's enumeration that includes zeros, and doesn't exclude
pairs whose gcd is not one.

                0,0  1,0  2,0  3,0  4,0
                0,1  1,1  2,1  3,1   
                0,2  1,2  2,2  3,2
                0,3  1,3  2,3  3,3
                0,4

in Cantor's ordering we get

    n  r c
    -  - -
    0  0,0
    1  1,0
    2  0,1            This gives us a formula:
    3  2,0
    4  1,1                  n = (r+c+1)*(r+c)/2 + c
    5  0,2
    6  3,0            With some work, this can be reversed to give
    7  2,1            a formula for r, c as a function of n
    8  1,2
    9  0,3                  cantor(r, c) = (r+c+1)*(r+c)/2 + c
   10  4,0
   11  3,1              anticantor(n) = the corresponding (r,c) pair
   12  2,2
   13  1,3
   14  0,4
     etc



The anti-Cantor calculation, n -> (r, c):
  diag = (int)floor(-0.5 + sqrt(1 + 8 * n) / 2);
  n0 = (diag + 1) * diag / 2.0;
  c = n - n0;
  r = diag - c;