---
id: 5900f4ef1000cf542c510001
title: 'Problem 386: Maximum length of an antichain'
challengeType: 5
forumTopicId: 302050
dashedName: problem-386-maximum-length-of-an-antichain
---

# --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

# --hints--

`euler386()` should return 528755790.

```js
assert.strictEqual(euler386(), 528755790);
```

# --seed--

## --seed-contents--

```js
function euler386() {

  return true;
}

euler386();
```

# --solutions--

```js
// solution required
```