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<?php

/*****************************

 * ProjectEuler - Problem 21

 * By Ross Marks

 *****************************

 * 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.

 ****************************/



$awns = 0;

$numbers = array();



for($i = 1; $i < 10000; $i++){

    $count = 0;

    $divisors = proper_divisors($i);

    foreach($divisors as $toadd)

        $count += $toadd;



    $numbers[$i] = $count;

}



foreach($numbers as $no => $div)

    if(@$numbers[$div] == $no && $no != $div)

        $awns += $div; 

    

echo "Awnser: $awns";





function proper_divisors($number){

    for ($n = 1; $n < ceil($number/2)+1; $n++)

        if (!($number % $n))

            $divisors[] = $n;



    return $divisors;

}

/*

array[$no] = $sum_of_divisors



-- loop to generate (0 - 10,000) ---



then loop array $key -> $val

  if array[$val] == $key // amicable pair found



add all pairs up to win

*/

?>

Project Euler Solutions by Ross Marks