Task 81

import math

def task81(n):
    d = {}
    last_prime = 2
    if n == 2:
        d = {2 : 1}
    else:
        while n > 1:
            if n%last_prime == 0 and d.get(last_prime) == None:
                d[last_prime] = 0 
            while n%last_prime == 0:
                d[last_prime]+=1
                n = int(n/last_prime)
            found_new = False
            for i in range(last_prime+1, int(math.sqrt(n)+1)):
                if n%i == 0:
                    found_new = True
                    last_prime = i #i should be prime, because if it can be divided to 2, then n can't divide to it, because all 2's were removed from n
                    break
            if not found_new:
                last_prime = n
    res = ""
    for i, d_i in enumerate(d):
        res += str(d_i)
        if d[d_i]!=1:
            res+="^{}".format(d[d_i])
        if i<len(d)-1:
            res+=" * "
    print(res)

# task81(199) -> 199
# task81(525) -> 3 * 5^2 * 7
# task81(2) -> 2
# task81(100) -> 2^2 * 5^2