// Example: 145 = 1! + 4! + 5! = 1 + 24 + 120 = 145
// Function to compute the factorial of a number
function factorial(n: number): number {
let fact: number = 1;
for (let 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
const factorials: number[] = Array.from({ length: 10 }, (_, i) => factorial(i));
// Define an upper limit (7 * 9! is a safe limit for this problem)
const upperLimit: number = 7 * factorials[9];
// Iterate through all numbers and check the condition
for (let num = 10; num <= upperLimit; num++) {
let sum: number = 0;
let temp: number = num;
// Calculate the sum of factorials of digits
while (temp > 0) {
const digit = temp % 10;
sum += factorials[digit];
temp = Math.floor(temp / 10);
}
// Check if the number equals the sum of the factorials of its digits
if (sum === num) {
console.log(`${num} is a digit factorial number.`);
}
}
}
findDigitFactorialNumbers();
/*
run:
"145 is a digit factorial number."
"40585 is a digit factorial number."
*/
