Tantalizing Function

tantalizing.php

<?php

/*
t(p) = max {n: n mod k = 0 for all k such that k^p <=n}

From https://twitter.com/republicofmath/status/574618883111411713

Basically, the question is, "is this function always finite?"
*/

//print_r( $argv);
$p = $argv[1];

$end = false;
$n = 1;
$set = array();
while (!$end) {
  $k = 1;
  //echo 'k^p = '.(pow($k,$p))."\n";
  $divisible = true;
  while (pow($k,$p) <= $n && $divisible) {
    echo "testing n = $n & k = $k\n";
    if ($n % $k != 0) {
      $divisible = false;
    }
    $k++;
  }
  if ($divisible) {
    $set[] = $n;
    if (isset($max)) {
      $diff = $n - $max;
    } else {
      $diff = 1;
    }
    $max = $n;
  } else {
    $diff = 1;
  }
  if ($n > 3*$max) $end = true;
  //$n++;
  $n += $diff;
}

echo "p = $p\n";
echo "n = $n\n";
echo "k = $k\n";
echo "set is\n";
print_r($set);