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+---
+title: Amicable pairs
+id: 5949b579404977fbaefcd737
+challengeType: 5
+forumTopicId: 302225
+---
+
+## Description
+<section id='description'>
+Two integers $N$ and $M$ are said to be <a href='https://en.wikipedia.org/wiki/Amicable numbers' title='wp: Amicable numbers' target='_blank'>amicable pairs</a> if $N \neq M$ and the sum of the <a href="https://rosettacode.org/wiki/Proper divisors" title="Proper divisors" target="_blank">proper divisors</a> of $N$ ($\mathrm{sum}(\mathrm{propDivs}(N))$) $= M$ as well as $\mathrm{sum}(\mathrm{propDivs}(M)) = N$.
+<strong>Example:</strong>
+<strong>1184</strong> and <strong>1210</strong> are an amicable pair, with proper divisors:
+<ul>
+  <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>
+</ul>
+</section>
+
+## Instructions
+<section id='instructions'>
+Calculate and show here the Amicable pairs below 20,000 (there are eight).
+</section>
+
+## Tests
+<section id='tests'>
+
+```yml
+tests:
+  - text: <code>amicablePairsUpTo</code> should be a function.
+    testString: assert(typeof amicablePairsUpTo === 'function');
+  - text: <code>amicablePairsUpTo(300)</code> should return <code>[[220,284]]</code>.
+    testString: assert.deepEqual(amicablePairsUpTo(300), answer300);
+  - text: <code>amicablePairsUpTo(3000)</code> should return <code>[[220,284],[1184,1210],[2620,2924]]</code>.
+    testString: assert.deepEqual(amicablePairsUpTo(3000), answer3000);
+  - text: <code>amicablePairsUpTo(20000)</code> should return <code>[[220,284],[1184,1210],[2620,2924],[5020,5564],[6232,6368],[10744,10856],[12285,14595],[17296,18416]]</code>.
+    testString: assert.deepEqual(amicablePairsUpTo(20000), answer20000);
+
+```
+
+</section>
+
+## Challenge Seed
+<section id='challengeSeed'>
+
+<div id='js-seed'>
+
+```js
+function amicablePairsUpTo(maxNum) {
+
+  return true;
+}
+```
+
+</div>
+
+
+### After Test
+<div id='js-teardown'>
+
+```js
+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]
+];
+```
+
+</div>
+
+</section>
+
+## Solution
+<section id='solution'>
+
+
+```js
+// amicablePairsUpTo :: Int -> [(Int, Int)]
+function amicablePairsUpTo(maxNum) {
+  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]
+function properDivisors(n) {
+  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]
+function range(m, n, step) {
+  const d = (step || 1) * (n >= m ? 1 : -1);
+
+  return Array.from({
+    length: Math.floor((n - m) / d) + 1
+  }, (_, i) => m + (i * d));
+}
+
+```
+
+</section>