I think C.
For example if n = 12 = 4*3
4-3 =1 (odd)
but if we take 1 also we can say n is also a prime number so it will have only 1 and n as factors.
N=12 will not fit the B and hence all such numbers that are not prime will be ruled out
12 has factors, 1,2,3,4,6,12
12-6 or 12-4 is NOT odd.
we need all factors difference to be odd. So even numbers are out
If you take 15, you will see that 15-5 = 10 and odd numbers are out too.
Only prime numbers remain and all prime numbers other than 2 will have a even difference