Erdős Problem #1196

The problem

Is it true that, for any $x$, if $A\subset [x,\infty)$ is a primitive set of integers (so that no distinct elements of $A$ divide each other) then

$$\sum_{a\in A}\frac{1}{a\log a}< 1+o(1),$$

where the $o(1)$ term $\to 0$ as $x\to \infty$?

Statement quoted from erdosproblems.com/1196, maintained by Thomas Bloom. Original source: [ESS68b][Er80,p.101]. Current status there: proved (Lean).

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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