If and .
Use the formula .
Note 's are odd (except possibly if there is a 2 factor) and so is even.
Thus for to be odd (if n is odd) it means we require .
Thus, and so .
For this NOT to be divisible by we require .
Thus, are all examples.
The other possibility is that , i.e. it has even factors.
For this NOT to be divisible by 4 we require .
But is even (by above) if .
Thus, are the only even ones not divisible by 4.