Given a positive integer $P>1$, let its prime factorization be written $$P=p_1^{a_1}p_2^{a_2}p_3^{a_3}...p_k^{a_k}$$

Define the functions $h(P)$ by $h(1)=1$ and $h(P)=min(a_1, a_2,..,a_k)$

> Is the follows property true or false?

> **The property**: *Let $n$ is a positive integer then $min(h(n), h(n+1), h(n+2)) = 1$*

**PS:** The property was checked up to $n=5.10^7$