Condition 1. 2n has four different prime number factors. If 2 was originally not a factor of n, n has 3 factors. If 2 was originally a factor of n, then n has 4 factors.
example : n=3*5*7, 2n=2*3*5*7 vs. n=2*3*5*7, 2n=2^2*3*5*7.
Condition 2. n^2 has four prime factors, so n has four prime factors. Again set n=2*3*5*7 n^2=2^2*3^2*5^2*7^2. n^2 still has four prime factors : 2,3,5,7