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Problem23.php
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Problem23.php
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<?php
/*
* Prompt: Find the sum of all the positive integers which cannot be written as the sum of two abundant numbers.
*
* Execute: php Problem23.php
*
* Answer: 4179871
*/
/* Returns:
* > 0 - Abundant Number
* 0 - Perfect Number
* < 0 - Deficient Number
*/
function d($n) {
$limit = sqrt($n);
$sumOfProperDivisors = 1;
if (floor($limit) == $limit) {
$sumOfProperDivisors = $limit * -1;
}
for ($i = 2; $i <= floor($limit); $i++) {
if ($n % $i == 0) {
$sumOfProperDivisors += $i + $n / $i;
}
}
return $sumOfProperDivisors - $n;
}
// #s greater than which can all be written as abundant numbers
$limit = 28123;
$abundantNumbers = [];
$sum = 0;
for ($i = 1; $i < $limit; $i++) {
if (d($i) > 0) {
// Put $i as index because it's faster to search by key below than value
$abundantNumbers[$i] = $i;
}
$canBeWrittenAsSum = false;
foreach ($abundantNumbers as $a) {
if (array_key_exists($i - $a, $abundantNumbers)) {
$canBeWrittenAsSum = true;
break;
}
}
if (!$canBeWrittenAsSum) {
$sum += $i;
}
}
echo $sum . PHP_EOL;