47 lines
935 B
Markdown
47 lines
935 B
Markdown
---
|
|
id: 5900f4fd1000cf542c51000f
|
|
title: 'Problem 401: Sum of squares of divisors'
|
|
challengeType: 5
|
|
forumTopicId: 302069
|
|
dashedName: problem-401-sum-of-squares-of-divisors
|
|
---
|
|
|
|
# --description--
|
|
|
|
The divisors of 6 are 1, 2, 3 and 6.
|
|
|
|
The sum of the squares of these numbers is $1 + 4 + 9 + 36 = 50$.
|
|
|
|
Let $\sigma_2(n)$ represent the sum of the squares of the divisors of $n$. Thus $\sigma_2(6) = 50$.
|
|
|
|
Let $\Sigma_2$ represent the summatory function of $\sigma_2$, that is $\Sigma_2(n) = \sum \sigma_2(i)$ for $i=1$ to $n$. The first 6 values of $\Sigma_2$ are: 1, 6, 16, 37, 63 and 113.
|
|
|
|
Find $\Sigma_2({10}^{15})$ modulo ${10}^9$.
|
|
|
|
# --hints--
|
|
|
|
`sumOfSquaresDivisors()` should return `281632621`.
|
|
|
|
```js
|
|
assert.strictEqual(sumOfSquaresDivisors(), 281632621);
|
|
```
|
|
|
|
# --seed--
|
|
|
|
## --seed-contents--
|
|
|
|
```js
|
|
function sumOfSquaresDivisors() {
|
|
|
|
return true;
|
|
}
|
|
|
|
sumOfSquaresDivisors();
|
|
```
|
|
|
|
# --solutions--
|
|
|
|
```js
|
|
// solution required
|
|
```
|