<?php
function countDivisors($x)
{
$divisors = 0;
$max = sqrt($x);
for ($i = 1; $i <= $max; ++$i) {
if ($x % $i == 0) {
$divisors += 2;
//print $i . "\n";
}
}
return $divisors;
}
$limit = 500;
for ($i = 1; true; ++$i) {
$x = $i * ($i + 1) / 2;
if (countDivisors($x) > $limit) {
print $x . "\n";
die;
}
}
* along with this program; if not, write to the Free Software
* Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston,
* MA 02110-1301, USA.
*
*
*/
function countDivisors($n)
{
$count = 0;
for ($i = 1; $i * $i <= $n; $i++) {
if ($n % $i == 0) {
if ($i * $i < $n) {
$count += 2;
} else {
$count += 1;
}
// $i == $n/$i is a divisor
}
}
return $count;
}
$n = 1;
while (countDivisors(($n + 1) / 2) * countDivisors($n) <= 500) {
$n++;
if (countDivisors($n / 2) * countDivisors($n + 1) > 500) {
break;
}
$n++;
}
$n = $n * ($n + 1) / 2;
echo "The first triangle number with over 500 divisors is {$n}\n";
