Hi, this is my solution to ECOO (2005) Fractorial using Python 3. Here is the problem,
Is there any improvements that I can make? I’d appreciate any advice. Thanks! 
Here’s my Python 3 code:
prime_list = [2]
fractorial = {}
def prime_factor(n):
prime_factorization = {}
for j in range(len(prime_list)):
while n % prime_list[j] == 0:
n = n // prime_list[j]
update_dict(prime_factorization, prime_list[j])
if len(prime_factorization) == 0:
update_dict(prime_factorization, n)
prime_list.append(n)
return prime_factorization
def update_dict(dict, n):
if n in dict:
dict[n] += 1
else:
dict[n] = 1
def main():
number = int(input())
if number == 1:
print("Fractorial(1) = 1")
else:
for i in range(2, number + 1):
prime_factorization = prime_factor(i)
for key in prime_factorization:
if key in fractorial:
if prime_factorization[key] > fractorial[key]:
fractorial[key] = prime_factorization[key]
else:
fractorial[key] = prime_factorization[key]
fractorial_value = 1
for key in fractorial:
fractorial_value *= key ** fractorial[key]
print(f"Fractorial({number}) = {fractorial_value}")
main()