# Example: 145 = 1! + 4! + 5! = 1 + 24 + 120 = 145
# Function to compute the factorial of a number
def factorial(n):
fact = 1
for i in range(2, n + 1):
fact *= i
return fact
# Function to find all numbers equal to the sum of the factorials of their digits
def find_digit_factorial_numbers():
# Precompute factorials of digits 0-9
factorials = [factorial(i) for i in range(10)]
# Define an upper limit (7 * 9! is a safe limit for this problem)
upper_limit = 7 * factorials[9]
# Iterate through all numbers and check the condition
for num in range(10, upper_limit + 1):
temp = num
digit_sum = 0
# Calculate the sum of factorials of digits
while temp > 0:
digit = temp % 10
digit_sum += factorials[digit]
temp //= 10
# Check if the number equals the sum of the factorials of its digits
if digit_sum == num:
print(f"{num} is a digit factorial number.")
find_digit_factorial_numbers()
'''
run:
145 is a digit factorial number.
40585 is a digit factorial number.
'''
