Problem Statement

Write a program which counts up from   1,   displaying each number as the multiplication of its prime factors. For the purpose of this task,   1   (unity)   may be shown as itself.

2   is prime,   so it would be shown as itself.       6   is not prime;   it would be shown as

2 × 3

{\displaystyle 2\times 3}

. 2144   is not prime;   it would be shown as

2 × 2 × 2 × 2 × 2 × 67

{\displaystyle 2\times 2\times 2\times 2\times 2\times 67}

.

Let's start with the solution:

def count_in_factors(n):
    if is_prime(n) or n == 1: 
        print(n,end="")
        return
    while n != 1:
        p = next_prime(1)
        while n % p != 0:
            p = next_prime(p)
        print(p,end="")
        n = n / p
        if n != 1: print(" x",end=" ")

for i in range(1, 101):
    print(i,"=",end=" ")
    count_in_factors(i)
    print("")