Problem 373

Circumscribed Circles

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(10⁷).

外接圆

每个三角形都有一个经过三个顶点的外接圆。考虑所有外接圆半径也是整数的整数边长三角形。

取其中外接圆半径不超过n的三角形，记它们的外接圆半径之和为S(n)。

已知S(100)=4950以及S(1200)=1653605。

求S(10⁷)。