cp's OEIS Frontend

For these odd primes delta(p) = A055034(n) = (p-1)/2 is squarefree, and therefore the (Abelian) multiplicative group Modd p (see a comment on A203571 for Modd n, not to be confused with mod n) is guaranteed to be cyclic. This is because the number of Abelian groups of order n (A000688) is 1 precisely for the squarefree numbers A005117. See also A210845. One can in fact prove that the multiplicative group Modd p is cyclic for all primes (the case p=2 is trivial). - Wolfdieter Lang, Sep 24 2012

The degree delta(m) of the minimal polynomial of rho(m) := 2*cos(Pi/m), called C(m,x) with coefficient array A187360, is given by A055034(m).

If delta(m) = phi(2*m)/2, m>=2, delta(1) = 1, with phi = A000010, is prime then the (Abelian) Galois group G(Q(rho(m))/Q) is cyclic. Because this Galois group of C(m,x) has order delta(m) this follows from a corollary to Lagrange's theorem, or also from Cauchy's theorem on groups.

Because the mentioned Galois group is isomorphic to the multiplicative group Modd m of order delta(m) (see a comment on A203571) all m = a(n) values appear in A206551.

This sequence is also a subsequence of A210845 because p is squarefree (see A005117).