The radical of $n$, $\operatorname{rad}(n)$, is the product of the distinct prime factors of $n$. For example, $504 = 2^3 \times 3^2 \times 7$, so $\operatorname{rad}(504) = 2 \times 3 \times 7 = 42$.

If we calculate $\operatorname{rad}(n)$ for $1 \le n \le 10$, then sort them on $\operatorname{rad}(n)$, and sorting on $n$ if the radical values are equal, we get:

Let $E(k)$ be the $k$-th element in the sorted $n$ column; for example, $E(4) = 8$ and $E(6) = 9$.

If $\operatorname{rad}(n)$ is sorted for $1 \le n \le 100000$, find $E(10000)$.