Let $\sigma(k)$ denote the sum of all positive divisors of $k$.
Consider the equation $\sigma(n+1)=\sigma(n)+1$.
Has it been investigated before? (I did some search in books avaliable for me, and in the internet, didn't found)
Does it have a solution except $n=2$ ?
I checked up to $10^7$, there are no other solutions in this interval.