A125867 Numbers k such that p=6k+1 is prime and cos(2*Pi/p) is an algebraic number of a 3-smooth degree, but not 2-smooth.

1, 2, 3, 6, 12, 16, 18, 27, 32, 72, 81, 96, 128, 192, 216, 243, 432, 486, 576, 648, 1728, 2048, 2916, 3072, 6561, 8748, 23328, 24576, 34992, 55296, 78732, 104976, 124416, 131072, 139968, 165888, 196608, 248832, 294912, 331776, 442368, 839808

Offset: 1

Author

Artur Jasinski, Dec 13 2006

Keywords

• nonn

Comments

Numbers k such that p=6k+1 is prime and the greatest prime divisor of p-1 is 3.

Crossrefs

Cf. A024899, A058383, A125866-A125878.

Programs

Mathematica

Do[If[Take[FactorInteger[EulerPhi[6n+1]][[ -1]], 1]=={3} && PrimeQ[6n+1],Print[n]],{n,1,100000}]

Extensions

Edited by Don Reble, Apr 24 2007