Question 67
Given two positive integers $m$ and $n$, show that there exist a positive integer $k$ and a set $S$ of at least $m$ multiples of $n$ such that the numbers $2^k \sigma(s)/s$, $s \in S$, are all odd; $\sigma(s)$ is the sum of all positive divisors of $s$ (1 and $s$ inclusive).