2018-09-30 22:01:58 +00:00
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---
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id: 5900f43f1000cf542c50ff52
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title: 'Problem 211: Divisor Square Sum'
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2020-11-27 18:02:05 +00:00
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challengeType: 5
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2019-08-05 16:17:33 +00:00
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forumTopicId: 301853
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2021-01-13 02:31:00 +00:00
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dashedName: problem-211-divisor-square-sum
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2018-09-30 22:01:58 +00:00
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---
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2020-11-27 18:02:05 +00:00
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# --description--
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2021-07-15 07:20:31 +00:00
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For a positive integer $n$, let $σ_2(n)$ be the sum of the squares of its divisors. For example,
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2018-09-30 22:01:58 +00:00
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2021-07-15 07:20:31 +00:00
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$$σ_2(10) = 1 + 4 + 25 + 100 = 130$$
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2018-09-30 22:01:58 +00:00
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2021-07-15 07:20:31 +00:00
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Find the sum of all $n$, $0 < n < 64\\,000\\,000$ such that $σ_2(n)$ is a perfect square.
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2018-09-30 22:01:58 +00:00
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2020-11-27 18:02:05 +00:00
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# --hints--
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2018-09-30 22:01:58 +00:00
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2021-07-15 07:20:31 +00:00
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`divisorSquareSum()` should return `1922364685`.
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2018-09-30 22:01:58 +00:00
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2020-11-27 18:02:05 +00:00
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```js
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2021-07-15 07:20:31 +00:00
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assert.strictEqual(divisorSquareSum(), 1922364685);
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2018-09-30 22:01:58 +00:00
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```
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2020-11-27 18:02:05 +00:00
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# --seed--
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2018-09-30 22:01:58 +00:00
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2020-11-27 18:02:05 +00:00
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## --seed-contents--
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2018-09-30 22:01:58 +00:00
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```js
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function divisorSquareSum() {
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2020-09-15 16:57:40 +00:00
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2018-09-30 22:01:58 +00:00
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return true;
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}
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2021-07-15 07:20:31 +00:00
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divisorSquareSum();
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2018-09-30 22:01:58 +00:00
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```
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2020-11-27 18:02:05 +00:00
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# --solutions--
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2018-09-30 22:01:58 +00:00
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```js
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// solution required
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```
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