Problem

Source: Mathcenter Contest / Oly - Thai Forum 2008 R2 p7 https://artofproblemsolving.com/community/c3196914_mathcenter_contest

Tags: number theory, sum of divisors



For every positive integer $n$, $\sigma(n)$ is equal to the sum of all the positive divisors of $n$ (for example, $\sigma(6)=1+2+3+6=12$) . Find the solution of the equation $$\sigma(p^2)=\sigma(q^b)$$where $p$ and $q$ are primes where $p>q$ and $b$ are positive integers. (gools)