General method for solving $\sigma(n) = x$. I'm looking for a general way to show all number n such that the sum of the divisors of n (including 1 and n itself) equal $x$.
For example, there is a question to show all the numbers such that $\sigma(n) = 28$ and I believe the only answer is 12, however, I'm not sure how to rigorously show that this is the only result (apart from manually going through every number, but there's surely a nicer way?). Is there a nicer general method for any $x$?
Thanks!