freeCodeCamp/curriculum/challenges/japanese/10-coding-interview-prep/project-euler/problem-464-mbius-function-and-intervals.md

id, title, challengeType, forumTopicId, dashedName

id	title	challengeType	forumTopicId	dashedName
5900f53d1000cf542c51004f	Problem 464: Möbius function and intervals	5	302139	problem-464-mbius-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 \times N(a, b) ≤ 100 \times P(a, b), and
• 99 \times P(a, b) ≤ 100 \times N(a, b).

For example, C(10) = 13, C(500) = 16\\,676 and C(10\\,000) = 20\\,155\\,319.

Find C(20\\,000\\,000).

--hints--

mobiusFunctionAndIntervals() should return 198775297232878.

assert.strictEqual(mobiusFunctionAndIntervals(), 198775297232878);

--seed--

--seed-contents--

function mobiusFunctionAndIntervals() {

  return true;
}

mobiusFunctionAndIntervals();

--solutions--

// solution required