The Möbius function, denoted $\mu (n)$, is defined as:

• $\mu (n)=(-1{)}^{\omega (n)}$ if $n$ is squarefree (where $\omega (n)$ is the number of distinct prime factors of $n$)
• $\mu (n)=0$ if $n$ is not squarefree.

Let $P(a,b)$ be the number of integers $n$ in the interval $[a,b]$ such that $\mu (n)=1$.
Let $N(a,b)$ be the number of integers $n$ in the interval $[a,b]$ such that $\mu (n)=-1$.
For example, $P(2,10)=2$ and $N(2,10)=4$.

Let $C(n)$ be the number of integer pairs $(a,b)$ such that:

• $1\le a\le b\le n$,
• $99\cdot N(a,b)\le 100\cdot P(a,b)$, and
• $99\cdot P(a,b)\le 100\cdot N(a,b)$.

For example, $C(10)=13$, $C(500)=16676$ and $C(10000)=20155319$.

Find $C(20000000)$.