While loop doesn't stop when number is power of 2

I have some issues in python console app. I coded an factorization console app. It works well, but when I input a number that is power of 2 like 4, 8, 16, the while loop doesn't stop. So it doesn't print anything and the code doesn't stop. Bellow is my code.

import math

n=input("Input check number:")
n=int(n)
sent= str(n) + "=1"

for m in range(2, int(n / 2)+1):
    if n % m == 0:
        k = n
        i = 0
        while k % m == 0:
            k = k / m
            i += 1
        sent = sent + "*" + str(m) + "^" + str(i)

if sent == str(n)+ "=1":
    sent = sent + "*" + str(n)

print(sent)

I want someone to help me. Thank you in advance.

The problem is that you don't change n or m inside the while loop. So, for example, for input n=4, m=2, k comes out to be n/m=2 which satisfies k%m==0 and since neither n nor m changes so it runs forever.

You can simplify the code by modifying n in the while loop to keep decreasing if it is divisible by the current divisor m. You can't do the same for k since k is reset to n again with the line k = n and it will start with the original number giving incorrect output.

Here is a bit modified version of the code with the outer while loop:

n=input("Input check number:")
n = int(n)
sent = str(n) + "=1"

m = 2  # start division with 2
while n > 1: # keep dividing till the number is greater than 1
    if m > n:
        break
    i = 0
    while n % m == 0:
        n = n / m   # modify n by dividing it with current divisor
        i += 1
    
    if i > 0: # add only if m divides n at least once
        sent = sent + "*" + str(m) + "^" + str(i)

    m = m + 1

if sent == str(n)+ "=1":
    sent = sent + "*" + str(n)

print(sent)

Output (for input 18):

18=1*2^1*3^2