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Found problems: 26

2018 Austria Beginners' Competition, 4
Tags: sum of divisors , number of divisors , number theory
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)