Constructible n-gons
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.
The challenge
Given an integer n>2, say if the n-gon is constructible or not.
Specification
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.
Examples
3 -> True
9 -> False
17 -> True
1024 -> True
65537 -> True
67109888 -> True
67109889 -> False
- 580
- 4
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