feat(21): complete amicable numbers

readme.md

@@ -39,7 +39,7 @@ Here is a [link to my profile](https://projecteuler.net/progress=newtykins).
 - [x] 18 - [Maximum path sum I](src/bin/18.rs)
 - [x] 19 - Counting Sundays
 - [x] 20 - Factorial digit sum
-- [ ] 21 - Amicable numbers
+- [x] 21 - Amicable numbers
 - [x] 22 - [Names scores](src/bin/22.rs)
 - [ ] 23 - Non-abundant sums
 - [ ] 24 - Lexicographic permutations

src/bin/21.rs

@@ -0,0 +1,44 @@
+/*
+Problem 21 - Amicable Numbers
+
+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 $a \ne b$, 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 $10000$.
+*/
+
+fn proper_divisors(number: usize) -> Vec<usize> {
+    let mut divisors = vec![1];
+
+    for divisor in 2..=(number / 2) {
+        if number % divisor == 0 {
+            divisors.push(divisor);
+        }
+    }
+
+    divisors
+}
+
+fn d(number: usize) -> usize {
+    proper_divisors(number).iter().sum()
+}
+
+fn amicable_numbers(upper_bound: usize) -> Vec<usize> {
+    let mut amicable_numbers = Vec::new();
+
+    for a in 2..upper_bound {
+        let b = d(a);
+
+        if a != b && d(b) == a {
+            amicable_numbers.push(a);
+        }
+    }
+
+    amicable_numbers
+}
+
+pub fn main() {
+    let sum = amicable_numbers(10_000).iter().sum::<usize>();
+
+    println!("The sum of the first 9,999 amicable numbers is {sum}!");
+}

src/commands/run.rs

@@ -44,6 +44,8 @@ mod three;
 mod twelve;
 #[path = "../bin/20.rs"]
 mod twenty;
+#[path = "../bin/21.rs"]
+mod twenty_one;
 #[path = "../bin/27.rs"]
 mod twenty_seven;
 #[path = "../bin/22.rs"]
@@ -90,6 +92,7 @@ pub async fn execute(
         67 => sixty_seven::main(),
         19 => nineteen::main(),
         20 => twenty::main(),
+        21 => twenty_one::main(),
         _ => {
             exists = false;
             println!(