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id	title	challengeType	forumTopicId	dashedName
5900f3e81000cf542c50fefb	Problem 124: Ordered radicals	5	301751	problem-124-ordered-radicals

--description--

The radical of n, rad(n), is the product of the distinct prime factors of n. For example, 504 = 2^3 × 3^2 × 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 k$th 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).

--hints--

orderedRadicals() should return 21417.

assert.strictEqual(orderedRadicals(), 21417);

--seed--

--seed-contents--

function orderedRadicals() {

  return true;
}

orderedRadicals();

--solutions--

// solution required

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