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