1.1 KiB
1.1 KiB
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·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).
--hints--
euler464()
should return 198775297232878.
assert.strictEqual(euler464(), 198775297232878);
--seed--
--seed-contents--
function euler464() {
return true;
}
euler464();
--solutions--
// solution required