---
id: 5900f5231000cf542c510035
challengeType: 5
title: 'Problem 439: Sum of sum of divisors'
---

## Description
<section id='description'>
Let d(k) be the sum of all divisors of k.
We define the function S(N) = ∑1≤i≤N ∑1≤j≤Nd(i·j).
For example, S(3) = d(1) + d(2) + d(3) + d(2) + d(4) + d(6) + d(3) + d(6) + d(9) = 59.

You are given that S(103) = 563576517282 and S(105) mod 109 = 215766508.
Find S(1011) mod 109.
</section>

## Instructions
<section id='instructions'>

</section>

## Tests
<section id='tests'>

```yml
tests:
  - text: <code>euler439()</code> should return 968697378.
    testString: 'assert.strictEqual(euler439(), 968697378, ''<code>euler439()</code> should return 968697378.'');'

```

</section>

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

<div id='js-seed'>

```js
function euler439() {
  // Good luck!
  return true;
}

euler439();
```

</div>



</section>

## Solution
<section id='solution'>

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