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

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

Is new n-conjecture as follows correct?

Conjecture: ${P_1,P_2,...,P_n}$ are positive integer and pairwise coprime, then:

$$\min\{h(P_1), h(P_2),...,h(P_n), h(P_1+P_2+...+P_n)\} \leq n+1$$

Case n=2 proposed two year ago at here Is the conjecture A+B=C following correct?. Now I reformulate as follows:

Let ${P_1,P_2}$ are coprime, then:

$$\min\{h(P_1), h(P_2), h(P_1+P_2)\} \leq 3$$