A constructible n-gon is a regular polygon with n sides that you can construct with only a compass and an unmarked ruler.
As stated by Gauss, the only n for which a n-gon is constructible is a product of any number of distinct Fermat primes and a power of 2 (ie.
n = 2^k * p1 * p2 * ... with
k being an integer and every
p some distinct Fermat prime).
A Fermat prime is a prime which can be expressed as F(n)=2^(2^n)+1 whith n a positive integer. The only known Fermat prime are for 0, 1, 2, 3 and 4.
Given an integer
n>2, say if the n-gon is constructible or not.
Your program or function should take an integer or a string representing said integer (either in unary, binary, decimal or any other base) and return or print a truthy or falsy value.
This is code-golf, so shortest answer wins, standard loopholes apply.
3 -> True 9 -> False 17 -> True 1024 -> True 65537 -> True 67109888 -> True 67109889 -> False