Erdős Problem #277 — The following extremal problem can now be posed: Put … where the maximum is to be taken over all the $m$ for which the divisors of $m$ do not form a covering system.

The following extremal problem can now be posed: Put

$$f(x) = \max_{m < x} \sigma(m)/m$$

where the maximum is to be taken over all the $m$ for which the divisors of $m$ do not form a covering system. By Haight's theorem $f(x)$ tends to infinity as $x \to \infty$. Is it true that $f(x) = o(\log\log x)$. In other words does $f(x)$ tend to infinity much slower than $\max \sigma(m)/m$.