CN-SMO 2020 Problem 5

Consider the set $I=\{ 1,2, \cdots, 2020 \}$ . Let $W= \{w(a,b)=(a+b)+ab | a,b \in I \} \cap I$ , $Y=\{y(a,b)=(a+b) \cdot ab | a,b \in I \} \cap I$ be its two subsets. Further, let $X= W \cap Y$ . (1) Find the sum of maximal and minimal elements in $X$ .(2) An element $n=y(a,b) (a \le b)$ in $Y$ is called excellent, if its representation is not unique (for instance, $20=y(1,5)=y(2,3)$ ). Find the number of excellent elements in $Y$ .