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

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

Unsorted			Sorted
n	rad(n)		n	rad(n)	k
1	1		1	1	1
2	2		2	2	2
3	3		4	2	3
4	2		8	2	4
5	5		3	3	5
6	6		9	3	6
7	7		5	5	7
8	2		6	6	8
9	3		7	7	9
10	10		10	10	10

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

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