Problem 124
Ordered radicals

The radical of n, rad(n), is the product of 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
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 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).

These problems are part of Project Euler and are licensed under CC BY-NC-SA 2.0 UK

http://projecteuler.net/problem=124