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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

Table of n, a(n) for n=1..56.

MATHEMATICA

Do[If[Take[FactorInteger[EulerPhi[2n+1]][[ -1]], 1]=={3}, Print[2n+1]], {n, 1, 10000}]

CROSSREFS

Cf. A004729, A051913, A058383, A125866-A125878.

Sequence in context: A196091 A222945 A129069 * A027692 A185720 A032487

Adjacent sequences:  A125863 A125864 A125865 * A125867 A125868 A125869

KEYWORD

nonn

AUTHOR

Artur Jasinski, Dec 13 2006

EXTENSIONS

Edited by Don Reble (djr(AT)nk.ca), Apr 24 2007

STATUS

approved

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Last modified April 20 06:17 EDT 2014. Contains 240779 sequences.