66 lines
1.1 KiB
Markdown
66 lines
1.1 KiB
Markdown
---
|
|
id: 5900f4ef1000cf542c510001
|
|
challengeType: 5
|
|
title: 'Problem 386: Maximum length of an antichain'
|
|
---
|
|
|
|
## Description
|
|
<section id='description'>
|
|
Let n be an integer and S(n) be the set of factors of n.
|
|
|
|
A subset A of S(n) is called an antichain of S(n) if A contains only one element or if none of the elements of A divides any of the other elements of A.
|
|
|
|
For example: S(30) = {1, 2, 3, 5, 6, 10, 15, 30}
|
|
{2, 5, 6} is not an antichain of S(30).
|
|
{2, 3, 5} is an antichain of S(30).
|
|
|
|
Let N(n) be the maximum length of an antichain of S(n).
|
|
|
|
Find ΣN(n) for 1 ≤ n ≤ 108
|
|
</section>
|
|
|
|
## Instructions
|
|
<section id='instructions'>
|
|
|
|
</section>
|
|
|
|
## Tests
|
|
<section id='tests'>
|
|
|
|
```yml
|
|
tests:
|
|
- text: <code>euler386()</code> should return 528755790.
|
|
testString: assert.strictEqual(euler386(), 528755790, '<code>euler386()</code> should return 528755790.');
|
|
|
|
```
|
|
|
|
</section>
|
|
|
|
## Challenge Seed
|
|
<section id='challengeSeed'>
|
|
|
|
<div id='js-seed'>
|
|
|
|
```js
|
|
function euler386() {
|
|
// Good luck!
|
|
return true;
|
|
}
|
|
|
|
euler386();
|
|
```
|
|
|
|
</div>
|
|
|
|
|
|
|
|
</section>
|
|
|
|
## Solution
|
|
<section id='solution'>
|
|
|
|
```js
|
|
// solution required
|
|
```
|
|
</section>
|