Prime Factorization

$\mathrm{\forall }n\in {\mathbb{Z}}_{\ge 2}\backslash forall\; n\; \backslash in\; \backslash Z\_\{\backslash ge2\}$, there exists an unqiue prime factorization such that:

n = (p1^k1)(p2^k2)(p3^k3)...

Prime Factorization in Wiki

Task

Given a positive integer n, create a function, perform the following procedure:

Factor n into its prime factors and calculate the sum of these factors.

Take the resulting sum and factor it into its prime factors, then compute the sum again.

Repeat this process until the result is a single prime number.

Example

sum_of_prime_factors(30) : (2)(3)(5) -> sum_of_prime_factors(2+3+5) : (2)(5) -> sum_of_prime_factors(2+5) : 7
#  should return 7

sum_of_prime_factors(18) : (2)(3^2) -> sum_of_prime_factors(2+3) : 5 #  The powers of prime numbers should be ignored.
#  should return 5

sum_of_prime_factors(314159) : 314159
#  should return 314159

Input/Output

• Type of input : int

• Range : $2\le n\le 10^{7}2\; \backslash le\; n\; \backslash le\; 10^7$