---
id: 5900f5261000cf542c510038
title: 'Problem 441: The inverse summation of coprime couples'
challengeType: 5
forumTopicId: 302113
dashedName: problem-441-the-inverse-summation-of-coprime-couples
---

# --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`.

```js
assert.strictEqual(inverseSummationCoprimeCouples(), 5000088.8395);
```

# --seed--

## --seed-contents--

```js
function inverseSummationCoprimeCouples() {

  return true;
}

inverseSummationCoprimeCouples();
```

# --solutions--

```js
// solution required
```