---
id: 5900f5231000cf542c510035
challengeType: 5
title: 'Problem 439: Sum of sum of divisors'
---
## 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.
## Instructions
## Tests
```yml
tests:
- text: euler439() should return 968697378.
testString: assert.strictEqual(euler439(), 968697378, 'euler439() should return 968697378.');
```
## Challenge Seed
```js
function euler439() {
// Good luck!
return true;
}
euler439();
```