problem 372 // project euler

Pencils of rays

Let R(M, N) be the number of lattice points (x, y) which satisfy M<x≤N, M<y≤N and $lfloor frac{y^2}{x^2} rfloor$ is odd.
We can verify that R(0, 100) = 3019 and R(100, 10000) = 29750422.
Find R(2·10⁶, 10⁹).

Note : $lfloor x rfloor$ represents the floor function.

光锥

记R(M, N)为满足M<x≤N、M<y≤N且$lfloor frac{y^2}{x^2} rfloor$为奇数的格点(x, y)的数目。
我们可以验证R(0, 100) = 3019以及R(100, 10000) = 29750422。
求R(2·10⁶, 10⁹)。

注：$lfloor x rfloor$表示下取整函数。