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%I #8 May 23 2022 03:55:06
%S 11,25,31,33,41,55,61,75,77,93,99,101,123,125,143,151,155,165,175,181,
%T 183,187,205,209,217,225,231,241,251,271,275,279,287,297,303,305,325,
%U 341,369,375,385,401,403,407,425,427,429,451,453,465,475,495,505,525
%N Odd numbers k such that cos(2*Pi/k) is an algebraic number of a 5-smooth degree, but not 3-smooth.
%C A regular polygon of a(n) sides can be constructed if one also has an angle trisector and 5-sector.
%t Do[If[Take[FactorInteger[EulerPhi[2n+1]][[ -1]],1]=={5},Print[2n+1]],{n,1,1000}]
%Y Cf. A058383, A061599, A125866-A125878.
%K nonn
%O 1,1
%A _Artur Jasinski_, Dec 13 2006
%E Edited by _Don Reble_, Apr 24 2007
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