Question 70
For any integer $n \ge 2$, denote by $s(n)$ the number of pairs of integers $(x, y)$, from $1, 2, \dots, n$, with $x \gt y$, such that $x$ and $y$ have exactly $x - y$ common divisors.
a)
Is there any $n$ such that $s(n) = 2019$?
b)
But for $s(n) = 2020$?
a)
Is there any $n$ such that $s(n) = 2019$?
b)
But for $s(n) = 2020$?