Finding a strong loop invariant

Question

Pseudocode:

if n < 2
    return false
while n != 1
    if n % 2 != 0
        return false
    n = n/2
return true

The loop will terminate when n is odd. If n = 1, true is returned and that means that n0 was a power of 2. Otherwise it's false.

I'm new at this and struggle with the proving the power of 2 part for before and during iterations and after the loop terminates. Also what does a loop invariant look like for a true vs false return on a loop?

Is it reasonable to say something like:

at the every iteration i, 1 <= n <= n0/(2^i)
true returned when n = 1 and n0 is a power of 2
false returned when n is odd and n > 1

Is it possible to even make strong loop invariant here without referencing the initial value of n?