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%I #8 Feb 03 2023 03:16:21
%S 1,2,3,6,12,16,18,27,32,72,81,96,128,192,216,243,432,486,576,648,1728,
%T 2048,2916,3072,6561,8748,23328,24576,34992,55296,78732,104976,124416,
%U 131072,139968,165888,196608,248832,294912,331776,442368,839808
%N 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.
%C Numbers k such that p=6k+1 is prime and the greatest prime divisor of p-1 is 3.
%t Do[If[Take[FactorInteger[EulerPhi[6n+1]][[ -1]], 1]=={3} && PrimeQ[6n+1],Print[n]],{n,1,100000}]
%Y Cf. A024899, A058383, A125866-A125878.
%K nonn
%O 1,2
%A _Artur Jasinski_, Dec 13 2006
%E Edited by _Don Reble_, Apr 24 2007