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 \times p_1 \times p_2 \times ...\$ with \$k\$ being an integer and every \$p_i\$ some distinct Fermat prime).
A Fermat prime is a prime which can be expressed as \$2^{2^n}+1\$ with \$n\$ a positive integer. The only known Fermat primes are for \$n = 0, 1, 2, 3 \text{ and } 4\$
The challenge
Given an integer \$n&gt;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.
Relevant OEIS
Examples
3 -&gt; True
9 -&gt; False
17 -&gt; True
1024 -&gt; True
65537 -&gt; True
67109888 -&gt; True
67109889 -&gt; False
Jelly, 7 5 bytes

Thanks to Sp3000 for saving 2 bytes.

ÆṪBSỊ


Uses the following classification:


  These are also the numbers for which phi(n) is a power of 2.


Where phi is Euler's totient function.

ÆṪ        # Compute φ(n).
  B       # Convert to binary.
   S      # Sum bits.
    Ị     # Check whether it's less than or equal to 1. This can only be the
          # case if the binary representation was of the form [1 0 0 ... 0], i.e. 
          e# a power of 2.


Try it online!

Alternatively (credits to xnor):

ÆṪ’BP
ÆṪ        # Compute φ(n).
  ’       # Decrement.
   B      # Convert to binary.
    P     # Product. This is 1 iff all bits in the binary representation are
          # 1, which means that φ(n) is a power of 2.


A direct port of my Mathematica answer is two bytes longer:

ÆṪ        # Compute φ(n).
  µ       # Start a new monadic chain, to apply to φ(n).
   ÆṪ     # Compute φ(φ(n)).
      H   # Compute φ(n)/2.
     =    # Check for equality.