Every triangle has a circumscribed circle that goes through the three vertices. Consider all integer sided triangles for which the radius of the circumscribed circle is integral as well.

Let $S(n)$ be the sum of the radii of the circumscribed circles of all such triangles for which the radius does not exceed $n$.

$S(100)=4950$ and $S(1200)=1653605$.

Find $S(10^7)$.