<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:
        
        isPrime = [True for _ in range(n + 1)]
        isPrime[0] = isPrime[1] = False

        i = 2
        while i * i <= n:
            if isPrime[i]:
                for j in range(i * i, n + 1, i):
                    isPrime[j] = False
            i += 1
        
        primeList = []
        primes = set()
        for i in range(n + 1):
            if isPrime[i]:
                primeList.append(i)
                primes.add(i)

        res = n
        while True:
            i = 0
            new = 0
            while i < len(primes):
                p = primeList[i]
                while n % p == 0:
                    new += p
                    n //= p
                if n in primes:
                    new += n
                    break
                i += 1
            if new != 0 and res > new:
                res = n = new
            else:
                break
        return res
328