---
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 $\sum N(n)$ for $1 ≤ n ≤ {10}^8$

# --hints--

`maximumLengthOfAntichain()` should return `528755790`.

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

# --seed--

## --seed-contents--

```js
function maximumLengthOfAntichain() {

  return true;
}

maximumLengthOfAntichain();
```

# --solutions--

```js
// solution required
```