Question 60
In the rectangular coordinate system every point with integer coordinates is called a lattice point. Let $P_n(n, n+5)$ be a lattice point and denote by $f(n)$ the number of lattice points on the open segment $\left(OP_n\right)$, where the point $O(0,0)$ is the coordinate system origin. Calculate the number $f(1) + f(2) + f(3) + \ldots + f(2002) + f(2003)$.