%I #8 May 23 2022 03:54:47
%S 53,79,131,157,159,169,237,265,313,371,393,395,471,477,507,521,547,
%T 553,583,655,677,689,711,785,795,845,859,869,901,911,917,937,939,1007,
%U 1027,1093,1099,1113,1171,1179,1183,1185,1219,1249,1301,1325,1343
%N Odd numbers k such that cos(2*Pi/k) is an algebraic number of a 13-smooth degree, but not 11-smooth.
%C A regular polygon of a(n) sides can be constructed if one also has an angle trisector, 5-, 7-, 11- and 13-sector.
%t Do[If[Take[FactorInteger[EulerPhi[2n+1]][[ -1]],1]=={13},Print[2n+1]],{n,1,10000}]
%Y Cf. A125866-A125878.
%K nonn
%O 1,1
%A _Artur Jasinski_, Dec 13 2006
%E Edited by _Don Reble_, Apr 24 2007