cp's OEIS Frontend

A125866 Odd numbers k such that cos(2*Pi/k) is an algebraic number of a 3-smooth degree, but not 2-smooth.

%I A125866 #18 May 23 2022 03:55:34
%S A125866 7,9,13,19,21,27,35,37,39,45,57,63,65,73,81,91,95,97,105,109,111,117,
%T A125866 119,133,135,153,163,171,185,189,193,195,219,221,243,247,259,273,285,
%U A125866 291,315,323,327,333,351,357,365,399,405,433,455,459,481,485,487,489
%N A125866 Odd numbers k such that cos(2*Pi/k) is an algebraic number of a 3-smooth degree, but not 2-smooth.
%C A125866 Odd terms of A051913.
%C A125866 This sequence is infinite (unlike A004729), because it contains any A058383(n) times any power of 3.
%C A125866 A regular polygon of a(n) sides can be constructed if one also has an angle trisector.
%H A125866 Robert Israel, <a href="/A125866/b125866.txt">Table of n, a(n) for n = 1..10000</a>
%p A125866 filter:= proc(n) local r,a,b;
%p A125866   r:= numtheory:-phi(n);
%p A125866   a:= padic:-ordp(r,2);
%p A125866   b:= padic:-ordp(r,3);
%p A125866   if b = 0 then return false fi;
%p A125866   r = 2^a*3^b;
%p A125866 end proc:
%p A125866 select(filter, [seq(i,i=3..1000,2)]); # _Robert Israel_, May 11 2020
%t A125866 Do[If[Take[FactorInteger[EulerPhi[2n+1]][[ -1]], 1]=={3},Print[2n+1]],{n,1,10000}]
%Y A125866 Cf. A004729, A051913, A058383, A125867-A125878.
%K A125866 nonn
%O A125866 1,1
%A A125866 _Artur Jasinski_, Dec 13 2006
%E A125866 Edited by _Don Reble_, Apr 24 2007