P13950 [EC Final 2019] Value

$\textit{Pang}$ believes that one cannot make an omelet without breaking eggs. For a subset $A$ of $\{1,2,\ldots,n\}$, we calculate the score of $A$ as follows: - Initialize the score as $0$. - For any $i\in A$, add $a_i$ to the score. - For any pair of integers $(i, j)$ satisfying $i\ge 2$, $j\ge 2$, $i\in A$ and $j\in A$, if there exists positive integer $k > 1$ such that $i^k=j$, subtract $b_j$ from the score. Find the maximum possible score over the choice of $A$.

The first line contains a single integer $n$ $(1\le n\le 100000)$. The second line contains $n$ integers $a_1,a_2,\ldots,a_n$ $(1\le a_i\le 1000000000)$. The third line contains $n$ integers $b_1,b_2,\ldots,b_n$ $(1\le b_i\le 1000000000)$.

Print a single integer $x$ --- the maximum possible score.