AT-OEMO-BEG 2018 Problem 4

For a positive integer $n$ we denote by $d(n)$ the number of positive divisors of $n$ and by $s(n)$ the sum of these divisors. For example, $d(2018)$ is equal to $4$ since $2018$ has four divisors $(1, 2, 1009, 2018)$ and $s(2018) = 1 + 2 + 1009 + 2018 = 3030$ . Determine all positive integers $x$ such that $s(x) \cdot d(x) = 96$ .

(Richard Henner)