--- 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(); ```
## Solution
```js // solution required ```