// Example: 145 = 1! + 4! + 5! = 1 + 24 + 120 = 145
// Function to compute the factorial of a number
function factorial(int $n): int {
$fact = 1;
for ($i = 2; $i <= $n; $i++) {
$fact *= $i;
}
return $fact;
}
// Function to find all numbers equal to the sum of the factorials of their digits
function findDigitFactorialNumbers(): void {
// Precompute factorials of digits 0-9
$factorials = [];
for ($i = 0; $i <= 9; $i++) {
$factorials[$i] = factorial($i);
}
// Define an upper limit (7 * 9! is a safe limit for this problem)
$upperLimit = 7 * $factorials[9];
// Iterate through all numbers and check the condition
for ($num = 10; $num <= $upperLimit; $num++) {
$sum = 0;
$temp = $num;
// Calculate the sum of factorials of digits
while ($temp > 0) {
$digit = $temp % 10;
$sum += $factorials[$digit];
$temp = intdiv($temp, 10);
}
// Check if the number equals the sum of the factorials of its digits
if ($sum === $num) {
echo "$num is a digit factorial number.\n";
}
}
}
findDigitFactorialNumbers();
/*
run:
145 is a digit factorial number.
40585 is a digit factorial number.
*/
