Problem Statement
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?
Categories:
Number Theory Powerful
Progress
Given in the 1986 Oberwolfach problem book as a problem of Erdős and Ivić.This is true when $r=2$, as proved by Heath-Brown [He88] (see [941]).
See [940] for the problem of which integers are the sum of at most $r$ many $r$-powerful numbers.
Source: erdosproblems.com/1107 | Last verified: January 19, 2026