login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 56th year, we are closing in on 350,000 sequences, and we’ve crossed 9,700 citations (which often say “discovered thanks to the OEIS”).

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 4 11:28 EST 2021. Contains 349486 sequences. (Running on oeis4.)