p21

inputs/passing/projEuler/p21.ts

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+import { factorize } from "./helpers/primes.ts";
+
+export default function main() {
+  let amicableNumbers = [];
+
+  for (let i = 2; i < 10_000; i++) {
+    if (isAmicable(i)) {
+      amicableNumbers.push(i);
+    }
+  }
+
+  return amicableNumbers.reduce((a, b) => a + b);
+}
+
+function isAmicable(n: number) {
+  const fSum = properFactorSum(n);
+
+  if (fSum === n) {
+    return false;
+  }
+
+  return properFactorSum(fSum) === n;
+}
+
+function factorizeAsPowers(n: number): [number, number][] {
+  const factors = factorize(n);
+
+  if (factors.length === 0) {
+    return [];
+  }
+
+  const result: [number, number][] = [];
+  let currentFactor = factors[0];
+  let currentPower = 1;
+
+  for (let i = 1; i < factors.length; i++) {
+    const factor = factors[i];
+
+    if (factor === currentFactor) {
+      currentPower += 1;
+    } else {
+      result.push([currentFactor, currentPower]);
+      currentFactor = factor;
+      currentPower = 1;
+    }
+  }
+
+  result.push([currentFactor, currentPower]);
+
+  return result;
+}
+
+function properFactorSum(n: number) {
+  const factors = factorizeAsPowers(n);
+  return 1 + factorSumMinus1(factors) - n;
+}
+
+function factorSumMinus1(factors: [number, number][]): number {
+  if (factors.length === 0) {
+    return 0;
+  }
+
+  const [factor, power] = factors[0];
+  let currentFactorSum = 0;
+
+  for (let i = 1; i <= power; i++) {
+    currentFactorSum += factor ** i;
+  }
+
+  const rest = factors.slice(1);
+
+  return currentFactorSum + (currentFactorSum + 1) * factorSumMinus1(rest);
+}