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 A125866 Odd numbers n such that cos(2Pi/n) is an algebraic number of a 3-smooth degree, but not 2-smooth. 14
 7, 9, 13, 19, 21, 27, 35, 37, 39, 45, 57, 63, 65, 73, 81, 91, 95, 97, 105, 109, 111, 117, 119, 133, 135, 153, 163, 171, 185, 189, 193, 195, 219, 221, 243, 247, 259, 273, 285, 291, 315, 323, 327, 333, 351, 357, 365, 399, 405, 433, 455, 459, 481, 485, 487, 489 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Odd terms of A051913. This sequence is infinite (unlike A004729), because it contains any A058383(n) times any power of 3. A regular polygon of a(n) sides can be constructed if one also has an angle trisector. LINKS Robert Israel, Table of n, a(n) for n = 1..10000 MAPLE filter:= proc(n) local r, a, b;   r:= numtheory:-phi(n);   a:= padic:-ordp(r, 2);   b:= padic:-ordp(r, 3);   if b = 0 then return false fi;   r = 2^a*3^b; end proc: select(filter, [seq(i, i=3..1000, 2)]); # Robert Israel, May 11 2020 MATHEMATICA Do[If[Take[FactorInteger[EulerPhi[2n+1]][[ -1]], 1]=={3}, Print[2n+1]], {n, 1, 10000}] CROSSREFS Cf. A004729, A051913, A058383, A125867-A125878. Sequence in context: A222945 A129069 A258616 * A027692 A343001 A297063 Adjacent sequences:  A125863 A125864 A125865 * A125867 A125868 A125869 KEYWORD nonn AUTHOR Artur Jasinski, Dec 13 2006 EXTENSIONS Edited by Don Reble, Apr 24 2007 STATUS approved

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Last modified April 16 09:04 EDT 2021. Contains 343030 sequences. (Running on oeis4.)