45 lines
906 B
Markdown
45 lines
906 B
Markdown
---
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id: 5900f45d1000cf542c50ff70
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title: 'Problem 241: Perfection Quotients'
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challengeType: 5
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forumTopicId: 301888
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dashedName: problem-241-perfection-quotients
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---
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# --description--
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For a positive integer $n$, let $σ(n)$ be the sum of all divisors of $n$, so e.g. $σ(6) = 1 + 2 + 3 + 6 = 12$.
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A perfect number, as you probably know, is a number with $σ(n) = 2n$.
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Let us define the perfection quotient of a positive integer as $p(n) = \frac{σ(n)}{n}$.
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Find the sum of all positive integers $n ≤ {10}^{18}$ for which $p(n)$ has the form $k + \frac{1}{2}$, where $k$ is an integer.
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# --hints--
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`perfectionQuotients()` should return `482316491800641150`.
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```js
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assert.strictEqual(perfectionQuotients(), 482316491800641150);
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```
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# --seed--
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## --seed-contents--
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```js
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function perfectionQuotients() {
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return true;
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}
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perfectionQuotients();
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```
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# --solutions--
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```js
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// solution required
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```
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