--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