074-DigitFactorialChains.py

#!/usr/bin/python3
# -*- coding: utf-8 -*-
# The number 145 is well known for the property that the sum of the factorial of its digits is equal to 145:
# 1! + 4! + 5! = 1 + 24 + 120 = 145
# Perhaps less well known is 169, in that it produces the longest chain of numbers that link back to 169; it turns out that there are only three such loops that exist:
# 169 → 363601 → 1454 → 169
# 871 → 45361 → 871
# 872 → 45362 → 872
# It is not difficult to prove that EVERY starting number will eventually get stuck in a loop. For example,
# 69 → 363600 → 1454 → 169 → 363601 (→ 1454)
# 78 → 45360 → 871 → 45361 (→ 871)
# 540 → 145 (→ 145)
# Starting with 69 produces a chain of five non-repeating terms, but the longest non-repeating chain with a starting number below one million is sixty terms.
# How many chains, with a starting number below one million, contain exactly sixty non-repeating terms?

from math import factorial

def factop(n):
    toplam = 0
    for i in str(n):
        toplam += factorial(int(i))
    return(toplam)
sonuc=0
for n in range(3,1000000):
    norg = n
    liste=[n]
    while(liste.count(factop(norg))!=1):
        faktoriyel=factop(norg)
        liste.append(faktoriyel)
        norg=faktoriyel
    if(len(liste)==60):
        sonuc += 1
print(sonuc)