Problem 938

Erdős Problem #938: declared status 'open'. Formalized: yes. Let $A=\{n_1<n_2<\cdots\}$ be the sequence of powerful numbers (if $p\mid n$ then $p^2\mid n$). Are there only finitely many three-term progressions of consecutive terms $n_k,n_{k+1},n_{k+2}$? Prize: no. OEIS: A001694. Tags: number theory.