A set S of positive integers is called magic if for any two distinct members of S, i and j,
\frac{i+j}{G C D(i, j)}
is also a member of S. The G C D, or greatest common divisor, of two positive integers is the largest integer that divides evenly into both of them; for example, G C D(36,80)=4.
Find and describe all finite magic sets.