MIT, fwiw, I did not want to type the optimal solution in case others wanted to play. The 16^2 was to show where a more “square” form of j+k and j-K might lead to and be the limit. A more “rectangular” form (if that makes visual sense) was to lead to an optimal shape with a maximum value for j+k.
My paper looked like this
252 1
126 2 ✓
84 3
63 4
42 6
36 7
18 14
Harder to explain than to do! My geometrical explanation might not make immediate sense. 