--description--

For an integer $M$, we define $R(M)$ as the sum of $\frac{1}{p·q}$ for all the integer pairs $p$ and $q$ which satisfy all of these conditions:

• $1 ≤ p < q ≤ M$
• $p + q ≥ M$
• $p$ and $q$ are coprime.

We also define $S(N)$ as the sum of $R(i)$ for $2 ≤ i ≤ N$.

We can verify that $S(2) = R(2) = \frac{1}{2}$, $S(10) ≈ 6.9147$ and $S(100) ≈ 58.2962$.

Find $S({10}^7)$. Give your answer rounded to four decimal places.

--hints--

inverseSummationCoprimeCouples() should return 5000088.8395.

assert.strictEqual(inverseSummationCoprimeCouples(), 5000088.8395);

--seed--

--seed-contents--

function inverseSummationCoprimeCouples() {

  return true;
}

inverseSummationCoprimeCouples();

--solutions--

// solution required