feat(euler): 21 - amicable numbers

challenges/euler/readme.md

@@ -32,7 +32,7 @@ The source code can be found in the [src](src) directory. My thoughts about some
 -   [x] [18 - Maximum path sum I](src/18%20-%20Maximum%20path%20sum%20I.ts)
 -   [x] [19 - Counting Sundays](src/19%20-%20Counting%20Sundays.ts)
 -   [x] [20 - Factorial digit sum](src/20%20-%20Factorial%20digit%20sum.ts)
--   [ ] 21 - Amicable numbers
+-   [x] [21 - Amicable numbers](src/21%20-%20Amicable%20numbers.ts)
 -   [ ] 22 - Names scores
 -   [ ] 23 - Non-abundant sums
 -   [ ] 24 - Lexicographic permutations

challenges/euler/src/21 - Amicable numbers.ts

@@ -0,0 +1,36 @@
+// Let d(n) be defined as the sum of proper divisors of n (numbers less than n which divide evenly into n).
+// If d(a) = b and d(b) = a, where a ≠ b, then a and b are an amicable pair and each of a and b are called amicable numbers.
+// For example, the proper divisors of 220 are 1, 2, 4, 5, 10, 11, 20, 22, 44, 55 and 110; therefore d(220) = 284. The proper divisors of 284 are 1, 2, 4, 71 and 142; so d(284) = 220.
+// Evaluate the sum of all the amicable numbers under 10000.
+export = {};
+
+const findProperDivisors = (number: number) => {
+    const divisors: number[] = [1];
+
+    for (let i = 2; i < number; i++) {
+        if (number % i === 0) {
+            divisors.push(i);
+        }
+    }
+
+    return divisors;
+};
+
+const d = (n: number) => findProperDivisors(n).reduce((a, b) => a + b);
+
+const findAmicableNumbers = (upperBound: number) => {
+    const amicableNumbers: number[] = [];
+
+    for (let a = 0; a < upperBound; a++) {
+        const b = d(a);
+
+        if (d(b) === a && a !== b) {
+            amicableNumbers.push(a);
+        }
+    }
+
+    return amicableNumbers;
+};
+
+// Output
+console.log(findAmicableNumbers(10000).reduce((a, b) => a + b));