Just write out the formula for .

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.

Then .

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.

(Where ).