Can we efficiently figure out when the sum of divisors of a number can be a prime?
I realized that this can be possible only when the number is expressible as a power of only one prime, e.g. $n = p^\alpha$. Now, the sum of divisors is $ 1+p+p^2+p^3+ \ldots + p^\alpha$. Now the problem is to figure out when this summation could be prime. How do we go about it?