prime_factors.py

from math import sqrt

def prime_factors(n):
    s = ""
    l = sorted(factorsList(n))
    l.append(-1)    # this addintional element helps the last element in l to appear in s
                    # but itself won't appear in s
    d = l[0]
    i = 0
    for n in l:
        if n == d:
            i += 1
        else:
            if i == 1:
                s += "(" + str(d) + ")"
            else:
                s += "(" + str(d) + "**" + str(i) + ")"
            i = 1
            d = n

    return s

def factorsList(n):
    if n == 1:
        return []

    for i in range(2, int(sqrt(n))+1):
        if n % i == 0:
            return [i] + factorsList(n//i)
    return [n]