Problem

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.

Solution

$sum = 0;

for ($i = 1; $i < 10000; $i++) {
  if ($i == d(d($i)) && $i != d($i)) {
    $sum += $i;
  }
}

echo $sum;

function d($num) {
  $temp = 0;

  for ($i = 1; $i <= $num / 2; $i++) {
    if ($num % $i == 0) {
      $temp += $i;
    }
  }

  return $temp;
}