# Problem 124: Ordered radicals
The radical of n, rad(n), is the product of the distinct prime factors
of n. For example, 504 = 23 × 32 × 7, so rad(504) = 2 × 3 × 7 = 42. If
we calculate rad(n) for 1 ≤ n ≤ 10, then sort them on rad(n), and
sorting on n if the radical values are equal, we get: Unsorted   Sorted
n rad(n) n rad(n) k 11   111 22   222 33   423 42   824 55   335 66  
936 77   557 82   668 93   779 1010   101010 Let E(k) be the kth element
in the sorted n column; for example, E(4) = 8 and E(6) = 9. If rad(n) is
sorted for 1 ≤ n ≤ 100000, find E(10000).