yaworsw/euler-manager

---
:id: 124
:name: Ordered radicals
:url: https://projecteuler.net/problem=124
:content: "The radical of _n_, rad(_n_), is the product of the distinct prime factors
  of _n_. For example, 504 = 2<sup>3</sup> × 3<sup>2</sup> × 7, so rad(504) = 2 ×
  3 × 7 = 42.\n\nIf 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:\n\n| \n**Unsorted**\n
  | &nbsp; | \n**Sorted**\n |\n| \n ![]({{ images_dir }}/spacer.gif)  \n**_n_**\n
  | \n ![]({{ images_dir }}/spacer.gif)  \n**rad(_n_)**\n | ![]({{ images_dir }}/spacer.gif)
  \ \n | \n ![]({{ images_dir }}/spacer.gif)  \n**_n_**\n | \n ![]({{ images_dir }}/spacer.gif)
  \ \n**rad(_n_)**\n | \n ![]({{ images_dir }}/spacer.gif)  \n**k**\n |\n| \n1\n |
  \n1\n | &nbsp; | \n1\n | \n1\n | \n1\n |\n| \n2\n | \n2\n | &nbsp; | \n2\n | \n2\n
  | \n2\n |\n| \n3\n | \n3\n | &nbsp; | \n4\n | \n2\n | \n3\n |\n| \n4\n | \n2\n |
  &nbsp; | \n8\n | \n2\n | \n4\n |\n| \n5\n | \n5\n | &nbsp; | \n3\n | \n3\n | \n5\n
  |\n| \n6\n | \n6\n | &nbsp; | \n9\n | \n3\n | \n6\n |\n| \n7\n | \n7\n | &nbsp;
  | \n5\n | \n5\n | \n7\n |\n| \n8\n | \n2\n | &nbsp; | \n6\n | \n6\n | \n8\n |\n|
  \n9\n | \n3\n | &nbsp; | \n7\n | \n7\n | \n9\n |\n| \n10\n | \n10\n | &nbsp; | \n10\n
  | \n10\n | \n10\n |\n\nLet E(_k_) be the _k_th element in the sorted _n_ column;
  for example, E(4) = 8 and E(6) = 9.\n\nIf rad(_n_) is sorted for 1 ≤ _n_ ≤ 100000,
  find E(10000).\n\n"