For natural number N,we can take the smallest and largest prime divisors and get the sum of them and repeat the process as many times as we want.For example N=3 => sum of the smallest and largest prime divisors is 3+3=6 =>

2+3=5 => 5+5=10 => 2+5=7 etc... Prove that we can get a square number by doing this for any natural N.

I noticed that if N is even the sum of the primes would be odd,and if it's odd the sum would be even.I think there's a pattern but can't figure out what it is.Help would be apprciated.