Prime Factoral Roots Inspired by digital roots, the prime factoral root of a number is the number that emerges when you take the prime factors of a number, add them together, and repeat the process on the resulting number, continuing until you end up with a prime number (which has itself as its only prime factor, and is thus its own prime factoral root).  The prime factoral root of 4 is 4, as 2*2=2+2, and this is the only non-prime prime factoral root of an integer greater than 1 (which is another special case, as it has no prime factors).  The OEIS sequence formed by prime factoral roots is A029908.  

For example, the prime factoral root of 24 is:

24=2*2*2*3

2+2+2+3=9=3*3

3+3=6=2*3

2+3=5, and the only prime factor of 5 is 5.  Therefore, the prime factoral root of 24 is 5.  


Your Task:

Write a program or function that finds the prime factoral root of an input integer.  

Input:

An integer, input through any reasonable method, between 2 and the largest integer your language will support (inclusive).  Specifically choosing a language that has an unreasonably low maximum integer size is not allowed (and also violates this standard loophole)

Output:

An integer, the prime factoral root of the input.  

Test Cases:

4   -&gt; 4
24  -&gt; 5
11  -&gt; 11
250 -&gt; 17


Scoring:

This is code-golf, lowest score in bytes wins!
05AB1E, 3 bytes

FÒO


Try it online!

Explanations:

FÒO   
F    Loops &lt;input&gt; times + 1
 Ò   List of prime factors w/ duplicates
  O  Total sum of the list
     -- implicit output