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 $n$?

gpt-erdos · GPT-5.2 Pro + Deep Research · unverified

Interpreting (\ast) as **Dirichlet convolution** (the usual meaning for arithmetic functions), [ (1_A\ast 1_A)(n)=\sum_{d\mid n} 1_A(d),1_A(n/d) ] counts the number of (ordered) factorizations $n=ab$ with (a,b\in A) (both powerful).

llm-hunter · gpt pro 5.2 · unverified

1 LLM attack(s) recorded (gpt pro 5.2); unverified.