MathDB

Call a lattice point visible if the line segment connecting the point and the origin does not pass through another lattice point. Given a positive integer

k

, denote by

S_k

the set of all visible lattice points

(x, y)

such that

x^2 + y^2 = k^2

. Let

D

denote the set of all positive divisors of

2021 \cdot 2025

. Compute the sum

\sum_{d \in D} |S_d|

Here, a lattice point is a point

(x, y)

on the plane where both

x

and

y

are integers, and

|A|

denotes the number of elements of the set

A

Problem Statement