---
id: 5900f5261000cf542c510038
challengeType: 5
title: 'Problem 441: The inverse summation of coprime couples'
---

## Description
<section id='description'>
For an integer M, we define R(M) as the sum of 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) = 1/2, S(10) ≈ 6.9147 and S(100) ≈ 58.2962.


Find S(107). Give your answer rounded to four decimal places.
</section>

## Instructions
<section id='instructions'>

</section>

## Tests
<section id='tests'>

```yml
tests:
  - text: <code>euler441()</code> should return 5000088.8395.
    testString: assert.strictEqual(euler441(), 5000088.8395, '<code>euler441()</code> should return 5000088.8395.');

```

</section>

## Challenge Seed
<section id='challengeSeed'>

<div id='js-seed'>

```js
function euler441() {
  // Good luck!
  return true;
}

euler441();
```

</div>



</section>

## Solution
<section id='solution'>

```js
// solution required
```
</section>