Erdős Problem #783

The problem

Fix some constant $C>0$ and let $N$ be large. Let $A\subseteq \{2,\ldots,N\}$ be such that $(a,b)=1$ for all $a\neq b\in A$ and $\sum_{n\in A}\frac{1}{n}\leq C$.

What choice of such an $A$ minimises the number of integers $m\leq N$ not divisible by any $a\in A$?

Statement quoted from erdosproblems.com/783, maintained by Thomas Bloom. Original source: [Er73,p.135]. Current status there: solved.

AI contributions

As recorded in Terence Tao's wiki AI contributions to Erdős problems (data as of 30 Jun 2026). 🟢 full, 🟡 partial, ⚪ unverified, 🔴 incorrect.

Caveats

The wiki's classifications are provisional and are not a benchmark. Many Erdős problems have never had a thorough literature review, so a result that looks new may later turn out to be known; some problems were also stated ambiguously or incorrectly. See the problem page for the full discussion.

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