# 2507. Smallest Value After Replacing With Sum of Prime Factors
###### tags: `Leetcode` `Medium` `Math` `Prime Factors`
Link: https://leetcode.com/problems/smallest-value-after-replacing-with-sum-of-prime-factors/description/
## 思路
如果我们能算出一个数n的所有prime factor的和s 然后令n=s 我们一直持续这个步骤 一直到n==s 就可以得到答案
那么重点就是如何计算一个数的所有prime factor

for(int i=2; i<=n; i++){
    while(n%i==0){
        n/=i;
    }
}

能进入到while回圈的每一个i都是prime factor
## Code

class Solution {
    public int smallestValue(int n) {
        while(true){
            int s = primes(n);
            if(n==s) break;
            n = s;
        }
        return n;
    }
    public int primes(int n) {
        int s = 0;
        for(int i=2; i<=n; i++){
            while(n%i==0){
                n/=i;
                s+=i;
            }
        }
        return s;
    }
}

class Solution:
    def smallestValue(self, n: int) -> int:
        def primes(n: int) -> int:
            s = 0
            for i in range(2, n+1):
                while n%i==0:
                    n /= i
                    s += i
            return s
        
        while n != (n:=primes(n)): pass
        return n