---
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>
