  Given a positive integer $n$, we let ${\rm sfp}(n)$ denote the squarefree
part of $n$. We determine all positive integers $n$ for which $\max \{ {\rm
sfp}(n), {\rm sfp}(n+1), {\rm sfp}(n+2) \} \leq 150$ by relating the problem to
finding integral points on elliptic curves. We also prove that there are
infinitely many $n$ for which \[
  \max \{ {\rm sfp}(n), {\rm sfp}(n+1), {\rm sfp}(n+2) \} < n^{1/3}. \]
