Problem 124 of Project Euler deals with radical functions, something I have never heard of before. So that always makes it interesting. It reads
The radical of n, rad(n), is the product of distinct prime factors of n. For example, 504 = 2^{3} x 3^{2} x 7, so rad(504) = 2 x 3 x 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). Continue reading →