98 lines
2.4 KiB
Markdown
98 lines
2.4 KiB
Markdown
---
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title: 'Abundant, deficient and perfect number classifications'
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id: 594810f028c0303b75339acd
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challengeType: 5
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forumTopicId: 302221
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---
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## Description
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<section id='description'>
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These define three classifications of positive integers based on their <a href='https://rosettacode.org/wiki/Proper divisors' title='Proper divisors' target='_blank'>proper divisors</a>.
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Let $P(n)$ be the sum of the proper divisors of <code>n</code> where proper divisors are all positive integers <code>n</code> other than <code>n</code> itself.
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If <code>P(n) < n</code> then <code>n</code> is classed as <code>deficient</code>
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If <code>P(n) === n</code> then <code>n</code> is classed as <code>perfect</code>
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If <code>P(n) > n</code> then <code>n</code> is classed as <code>abundant</code>
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<strong>Example</strong>:
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<code>6</code> has proper divisors of <code>1</code>, <code>2</code>, and <code>3</code>.
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<code>1 + 2 + 3 = 6</code>, so <code>6</code> is classed as a perfect number.
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</section>
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## Instructions
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<section id='instructions'>
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Implement a function that calculates how many of the integers from <code>1</code> to <code>20,000</code> (inclusive) are in each of the three classes. Output the result as an array in the following format <code>[deficient, perfect, abundant]</code>.
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</section>
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## Tests
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<section id='tests'>
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```yml
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tests:
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- text: <code>getDPA</code> should be a function.
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testString: assert(typeof getDPA === 'function');
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- text: <code>getDPA</code> should return an array.
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testString: assert(Array.isArray(getDPA(100)));
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- text: <code>getDPA</code> return value should have a length of 3.
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testString: assert(getDPA(100).length === 3);
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- text: <code>getDPA(20000)</code> should equal [15043, 4, 4953]
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testString: assert.deepEqual(getDPA(20000), solution);
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```
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</section>
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## Challenge Seed
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<section id='challengeSeed'>
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<div id='js-seed'>
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```js
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function getDPA(num) {
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}
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```
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</div>
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### After Test
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<div id='js-teardown'>
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```js
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const solution = [15043, 4, 4953];
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```
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</div>
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</section>
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## Solution
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<section id='solution'>
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```js
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function getDPA(num) {
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const dpa = [1, 0, 0];
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for (let n = 2; n <= num; n += 1) {
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let ds = 1;
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const e = Math.sqrt(n);
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for (let d = 2; d < e; d += 1) {
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if (n % d === 0) {
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ds += d + (n / d);
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}
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}
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if (n % e === 0) {
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ds += e;
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}
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dpa[ds < n ? 0 : ds === n ? 1 : 2] += 1;
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}
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return dpa;
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}
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```
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</section>
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