problem-034.py

### Problem 34 - Digit Factorials
###-----------------------------------------------------------------------------------------
### 145 is a curious number, as 1! + 4! + 5! = 1 + 24 + 120 = 145.
### Find the sum of all numbers which are equal to the sum of the factorial of their digits.
### Note: as 1! = 1 and 2! = 2 are not sums they are not included.

### Solution

# 7*9! = 2540160 which is less than 9999999 so we will set this as the upper limit

factorials = {
    "0": 1,
    "1": 1,
    "2": 2,
    "3": 6,
    "4": 24,
    "5": 120,
    "6": 720,
    "7": 5040,
    "8": 40320,
    "9": 362880,
}
total_sum = 0

for i in range(3, 2540161):
    factorial_sum = 0
    for j in str(i):
        factorial_sum += factorials[j]
    if i == factorial_sum:
        total_sum += i

print("Total digit factorial sum: " + str(total_sum))