<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>

def is_prime(n, table):
    return table[n] == n

def factorize(n, table):
    factors = []
    while n > 1:
        factors.append(table[n])
        n //= table[n]
    return factors

def take_step(n, table):
    factors = factorize(n, table)
    return sum(factors)

def build_table(n):
    table = [None] * (n+1)
    table[1] = 1
    for i in range(2, n+1):
        if table[i] is not None:
            continue
        for j in range(i, n+1, i):
            if table[j] is not None:
                continue
            table[j] = i
    return table

class Solution:
    def smallestValue(self, n: int) -> int:
        table = build_table(n)
        minv = n
        while not is_prime(n, table):
            #print('n:', n)
            x = take_step(n, table)
            minv = min(minv, x)
            if x == n:
                break
            n = x
        return minv

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