Problem #277: Is it true that, for every $c$, there exists an $n$ such...

Is it true that, for every $c$, there exists an $n$ such that $\sigma(n)>cn$ but there is no covering system whose moduli all divide $n$?

SOLVED

Problem Statement

Is it true that, for every $c$, there exists an $n$ such that $\sigma(n)>cn$ but there is no covering system whose moduli all divide $n$?

Categories: Number Theory Covering Systems

This was answered affirmatively by Haight [Ha79].

Source: erdosproblems.com/277 | Last verified: January 14, 2026