Question 41
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
$$
\sum_{d \in D}\left|S_{d}\right|
$$
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 $A$.
$$
\sum_{d \in D}\left|S_{d}\right|
$$
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 $A$.