---
id: 5900f4ef1000cf542c510001
challengeType: 5
title: '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
## Instructions
## Tests
```yml
tests:
- text: euler386() should return 528755790.
testString: assert.strictEqual(euler386(), 528755790, 'euler386() should return 528755790.');
```
## Challenge Seed
```js
function euler386() {
// Good luck!
return true;
}
euler386();
```