Erdős Problem #943

The problem

Let $A$ be the set of powerful numbers (if $p\mid n$ then $p^2\mid n$). Is it true that

$$1_A\ast 1_A(n)=n^{o(1)}$$

for every $n$?

Statement quoted from erdosproblems.com/943, maintained by Thomas Bloom. Original source: [Er76d]. Current status there: open.

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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