Let S be the set of ordered integer pairs (x, y) such that 0<x<y<42 and there exists some integer n such that x^{6}-y^{6} \mid n^{2}+2015^{2}. What is the sum \sum_{\left(x_{i}, y_{i}\right) \in S} x_{i} y_{i}?
Let S be the set of ordered integer pairs (x, y) such that 0<x<y<42 and there exists some integer n such that x^{6}-y^{6} \mid n^{2}+2015^{2}. What is the sum \sum_{\left(x_{i}, y_{i}\right) \in S} x_{i} y_{i}?