IN-TST 2002 Problem 8

Let $\sigma(n)=\sum_{d|n} d$ , the sum of positive divisors of an integer $n>0$ . [list](a) Show that $\sigma(mn)=\sigma(m)\sigma(n)$ for positive integers $m$ and $n$ with $gcd(m,n)=1$ (b) Find all positive integers $n$ such that $\sigma(n)$ is a power of $2$ .[/list]