OPEN

What is the largest possible subset $A\subseteq\{1,\ldots,N\}$ which contains $N$ such that $(a,b)=1$ for all $a\neq b\in A$?

A problem of Erdős and Graham. They conjecture that this maximum is either $N/p$ (where $p$ is the smallest prime factor of $N$) or it is the number of integers $\{2t: t\leq N/2\textrm{ and }(t,N)=1\}$.