021.js

// 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.

function properDivisorSum(n) {
    var sum = 0;
    for (var i = 1; i <= n/2; i++) {
        if (n % i === 0) {
            sum += i;
        }
    }
    return sum;
}

function findAmicablesSum(n) {
    var sum = 0;
    var j;
    for (var i = 1; i <= n; i++) {
        j = properDivisorSum(i);
        if (j > n || j === i) continue;
        if (properDivisorSum(j) === i) {
            sum = sum + i + j;
        }
    }
    return sum / 2;
}

console.log( findAmicablesSum(10000) );