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---
id: 5949b579404977fbaefcd737
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title: Amicable pairs
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challengeType: 5
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forumTopicId: 302225
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dashedName: amicable-pairs
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---
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# --description--
Two integers $N$ and $M$ are said to be [amicable pairs ](<https://en.wikipedia.org/wiki/Amicable numbers> "wp: Amicable numbers" ) if $N \\neq M$ and the sum of the [proper divisors ](<https://rosettacode.org/wiki/Proper divisors> "Proper divisors" ) of $N$ ($\\mathrm{sum}(\\mathrm{propDivs}(N))$) $= M$ as well as $\\mathrm{sum}(\\mathrm{propDivs}(M)) = N$.
**Example:**
**1184** and **1210** are an amicable pair, with proper divisors:
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< ul >
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< li > 1, 2, 4, 8, 16, 32, 37, 74, 148, 296, 592 and< / li >
< li > 1, 2, 5, 10, 11, 22, 55, 110, 121, 242, 605 respectively.< / li >
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< / ul >
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# --instructions--
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Calculate and show here the Amicable pairs below 20,000 (there are eight).
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# --hints--
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`amicablePairsUpTo` should be a function.
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```js
assert(typeof amicablePairsUpTo === 'function');
```
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`amicablePairsUpTo(300)` should return `[[220,284]]` .
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```js
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assert.deepEqual(amicablePairsUpTo(300), answer300);
```
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`amicablePairsUpTo(3000)` should return `[[220,284],[1184,1210],[2620,2924]]` .
```js
assert.deepEqual(amicablePairsUpTo(3000), answer3000);
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```
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`amicablePairsUpTo(20000)` should return `[[220,284],[1184,1210],[2620,2924],[5020,5564],[6232,6368],[10744,10856],[12285,14595],[17296,18416]]` .
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```js
assert.deepEqual(amicablePairsUpTo(20000), answer20000);
```
# --seed--
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## --after-user-code--
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```js
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const answer300 = [[220, 284]];
const answer3000 = [
[220, 284],
[1184, 1210],
[2620, 2924]
];
const answer20000 = [
[220, 284],
[1184, 1210],
[2620, 2924],
[5020, 5564],
[6232, 6368],
[10744, 10856],
[12285, 14595],
[17296, 18416]
];
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```
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## --seed-contents--
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```js
function amicablePairsUpTo(maxNum) {
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return true;
}
```
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# --solutions--
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```js
// amicablePairsUpTo :: Int -> [(Int, Int)]
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function amicablePairsUpTo(maxNum) {
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return range(1, maxNum)
.map(x => properDivisors(x)
.reduce((a, b) => a + b, 0))
.reduce((a, m, i, lst) => {
const n = i + 1;
return (m > n) & & lst[m - 1] === n ?
a.concat([
[n, m]
]) : a;
}, []);
}
// properDivisors :: Int -> [Int]
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function properDivisors(n) {
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if (n < 2 ) return [ ] ;
const rRoot = Math.sqrt(n);
const intRoot = Math.floor(rRoot);
const blnPerfectSquare = rRoot === intRoot;
const lows = range(1, intRoot)
.filter(x => (n % x) === 0);
return lows.concat(lows.slice(1)
.map(x => n / x)
.reverse()
.slice(blnPerfectSquare | 0));
}
// Int -> Int -> Maybe Int -> [Int]
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function range(m, n, step) {
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const d = (step || 1) * (n >= m ? 1 : -1);
return Array.from({
length: Math.floor((n - m) / d) + 1
}, (_, i) => m + (i * d));
}
```