2507. Smallest Value After Replacing With Sum of Prime Factors

Problem Link

Description

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You are given a positive integer n.

Continuously replace n with the sum of its prime factors.

• Note that if a prime factor divides n multiple times, it should be included in the sum as many times as it divides n.

Return the smallest value n will take on.

 

Example 1:

Input: n = 15
Output: 5
Explanation: Initially, n = 15.
15 = 3 * 5, so replace n with 3 + 5 = 8.
8 = 2 * 2 * 2, so replace n with 2 + 2 + 2 = 6.
6 = 2 * 3, so replace n with 2 + 3 = 5.
5 is the smallest value n will take on.

Example 2:

Input: n = 3
Output: 3
Explanation: Initially, n = 3.
3 is the smallest value n will take on.

 

Constraints:

• 2 <= n <= 105

Solution

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Python3

class Solution:
    def smallestValue(self, n: int) -> int:
        vis = set()
        
        while n not in vis:
            vis.add(n)
            
            k = 0
            
            for factor in range(2, n + 1):
                while n % factor == 0:
                    k += factor
                    n //= factor
            
            n = k
 
        return n