<p>You are given a positive integer <code>n</code>.</p>

<p>Continuously replace <code>n</code> with the sum of its <strong>prime factors</strong>.</p>

<ul>
	<li>Note that if a prime factor divides <code>n</code> multiple times, it should be included in the sum as many times as it divides <code>n</code>.</li>
</ul>

<p>Return <em>the smallest value </em><code>n</code><em> will take on.</em></p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> n = 15
<strong>Output:</strong> 5
<strong>Explanation:</strong> 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.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> n = 3
<strong>Output:</strong> 3
<strong>Explanation:</strong> Initially, n = 3.
3 is the smallest value n will take on.
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>2 &lt;= n &lt;= 10<sup>5</sup></code></li>
</ul>

class Solution:
    def smallestValue(self, n: int) -> int:
        arr=[-1 for _ in range(n+1)]
        arr[0]="P"
        arr[1]="P"
        for i in range(len(arr)):
            if arr[i]==-1:
                arr[i]="P"
                j=i+i
                while j<len(arr):
                    if arr[j]==-1:
                        arr[j]="N"
                    j+=i
        prime=[]
        for i in range(2,len(arr)):
            if arr[i]=="P":
                prime.append(i)
        prev=set()
        while n not in prime:
            if n not in prev:prev.add(n)
            else:return n
            
            total=0
            for p in prime:
                if n%p!=0:
                    continue
                else:
                    while n%p==0:
                        total+=p
                        n=n//p
            n=total
        return n
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