freeCodeCamp/curriculum/challenges/english/08-coding-interview-prep/project-euler/problem-464-mbius-function-and-intervals.english.md

---
id: 5900f53d1000cf542c51004f
challengeType: 5
title: 'Problem 464: Möbius function and intervals'
---

## Description
<section id='description'>
The Möbius function, denoted μ(n), is defined as:
μ(n) = (-1)ω(n) if n is squarefree (where ω(n) is the number of distinct prime factors of n)
μ(n) = 0 if n is not squarefree.

Let P(a,b) be the number of integers n in the interval [a,b] such that μ(n) = 1.
Let N(a,b) be the number of integers n in the interval [a,b] such that μ(n) = -1.
For example, P(2,10) = 2 and N(2,10) = 4.



Let C(n) be the number of integer pairs (a,b) such that:
 1 ≤ a ≤ b ≤ n,
 99·N(a,b) ≤ 100·P(a,b), and
 99·P(a,b) ≤ 100·N(a,b).

For example, C(10) = 13, C(500) = 16676 and C(10 000) = 20155319.



Find C(20 000 000).
</section>

## Instructions
<section id='instructions'>

</section>

## Tests
<section id='tests'>

```yml
tests:
  - text: <code>euler464()</code> should return 198775297232878.
    testString: assert.strictEqual(euler464(), 198775297232878, '<code>euler464()</code> should return 198775297232878.');

```

</section>

## Challenge Seed
<section id='challengeSeed'>

<div id='js-seed'>

```js
function euler464() {
  // Good luck!
  return true;
}

euler464();
```

</div>



</section>

## Solution
<section id='solution'>

```js
// solution required
```
</section>