# Problem 464: Möbius function and intervals
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).