---
id: 5900f53d1000cf542c51004f
challengeType: 5
title: 'Problem 464: Möbius function and intervals'
---
## 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).
## Instructions
## Tests
```yml
tests:
- text: euler464() should return 198775297232878.
testString: assert.strictEqual(euler464(), 198775297232878, 'euler464() should return 198775297232878.');
```
## Challenge Seed
```js
function euler464() {
// Good luck!
return true;
}
euler464();
```