On near superperfect numbers, the Goormaghtigh conjecture, and Mertens' theorem

Satvik Beri, Joshua Zelinsky

Let $\sigma (n)$ be the sum of the divisors of $n$. Kalita and Saikia defined a number $n$ to be near superperfect if $2n+d=\sigma (\sigma (n))$ for some positive divisor $d$ of $n$. We extend some…