function q21($from, $to)
{
$integerToSum = [];
for ($i = $from; $i < $to; ++$i) {
$primeDecomposition = IntegerFactorization::solve($i);
$sumOfDivisors = Math::divisorsSum($primeDecomposition);
$sumOfProperDivisors = $sumOfDivisors - $i;
$integerToSum[$i] = $sumOfProperDivisors;
}
$sumOfAmicableNumbers = 0;
foreach ($integerToSum as $integer => $sum) {
if ($integer !== $sum && isset($integerToSum[$sum]) && $integerToSum[$sum] === $integer) {
$sumOfAmicableNumbers += $integerToSum[$integer] + $integerToSum[$sum];
unset($integerToSum[$integer]);
unset($integerToSum[$sum]);
}
}
return $sumOfAmicableNumbers;
}
public static function greatestCommonDivisor(array $numbers)
{
if (empty($numbers)) {
throw new LogicException('Cannot obtain greatest common divisor on an empty array.');
}
$factors = [];
foreach ($numbers as $number) {
$decomposition = IntegerFactorization::solve($number);
foreach ($decomposition as $prime => $count) {
$factors[$prime][] = $count;
}
}
$total = 1;
foreach ($factors as $prime => $counts) {
if (count($counts) === 1) {
continue;
}
sort($counts);
$total *= $prime ** $counts[0];
}
return $total;
}
