prime_factors.py

from collections import defaultdict, Counter, deque
import math

def primeFac(n):
    prime_list = deque()
    pivot = 2
    current = n
    while current != 1 and pivot <= math.sqrt(n):
        if current % pivot == 0:
            prime_list.append(pivot)
            current //= pivot
        else:
            pivot += 1
    if pivot > math.sqrt(n):
        prime_list.append(current)
    return prime_list
    
        
def generate_expression(l):
    amounts = Counter(l)
    return "".join(["({}**{})".format(i, amounts[i]) if amounts[i] !=1 else "({})".format(i) for i in sorted(amounts.keys())])
    
    
def primeFactors(n): 
    l = primeFac(n)
    exp = generate_expression(l)
    print (exp)
    return exp