# Amicable pairs

## Solutions

Solution 1 (Click to Show/Hide)
``````// Get sum of factors
function getSumOfFacts(num) {
let sum = 1; // 1 is always a divisor
// Optimization Trick - Factors come in pairs up to the sqrt of num
let upperBound = Math.floor(Math.sqrt(num));
for (let i = 2; i <= upperBound; i++) {
if (num % i === 0) {
sum += i;
sum += num / i;
}
}
// Remove sqrt if factor to prevent double counting
if (upperBound === Math.sqrt(num)) {
sum -= upperBound;
}
return sum;
}

// Test if number has amicalbe pair
function getAmicablePairValueInBound(a, bound) {
const sumA = getSumOfFacts(a);
if (sumA !== a && sumA <= bound && getSumOfFacts(sumA) === a) {
return [true, sumA];
}
return [false, 0];
}

// Get amicable pairs
function amicablePairsUpTo(maxNum) {
const amicablePairs = [];
for (let i = 1; i < maxNum; i++) {
const [hasPair, pairValue] = getAmicablePairValueInBound(i, maxNum);
if (hasPair && pairValue > i) {
amicablePairs.push([i, pairValue]);
}
}
return amicablePairs;
}
``````