Project Euler #254

Define f(n) as the sum of the factorials of the digits of n. For example, f(342) = 3! + 4! + 2! = 32.

Define sf(n) as the sum of the digits of f(n). So sf(342) = 3 + 2 = 5.

Define g(i) to be the smallest positive integer n such that sf(n) = i. Though sf(342) is 5, sf(25) is also 5, and it can be verified that g(5) is 25.

Define sg(i) as the sum of the digits of g(i). So sg(5) = 2 + 5 = 7.

Further, it can be verified that g(20) is 267 and ∑ sg(i) for 1 ≤ i ≤ 20 is 156.

What is ∑ sg(i) for 1 ≤ i ≤ 150?

def factorial(n):
    
    if n == 1:        
        return n

    elif n < 1:
        return 0

    else:
        return n*factorial(n-1)

def f(x):
    
    x = [int(i) for i in str(x)]
    
    sum = 0
    
    for j in range(len(x)):
        
        sum = sum + factorial(x[j])
    
    return sum

def sf(x):
    
    x = f(x)
    
    x = [int(i) for i in str(x)]
    
    sum = 0
    
    for j in range(len(x)):
        
        sum = sum + int(x[j])
    
    return sum

def g(x):
    
    count = 0
    
    while sf(count) < x:
        
        count += 1
    
    return count
    
def sg(x):
    
    l = g(x)
    
    y = [int(i) for i in str(l)]
    
    sum = 0
    
    for i in range(len(y)):
        
        sum = sum + y[i]
    
    return sum

def finalanswer(n):
    answer = 0

    for i in range(n):
        
        answer = answer + sg(i)

    return(answer)