

A125866


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


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
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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, A125867A125878.
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



