Problem 1107

Erdős Problem #1107: declared status 'open'. Formalized: yes. Let $r\geq 2$. A number $n$ is $r$-powerful if for every prime $p$ which divides $n$ we have $p^r\mid n$. Is every large integer the sum of at most $r+1$ many $r$-powerful numbers? Prize: no. OEIS: A056828, A392342, A392343. Tags: number theory, powerful.