Problem Statement
Let $f(n)$ count the number of solutions to $k\sigma(k)=n$, where $\sigma(k)$ is the sum of divisors of $k$. Is it true that $f(n)\leq n^{o(\frac{1}{\log\log n})}$? Perhaps even $\leq (\log n)^{O(1)}$?
Categories:
Number Theory
Progress
This is discussed in problem B11 of Guy's collection [Gu04].Source: erdosproblems.com/1060 | Last verified: January 19, 2026