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A125866
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Odd numbers n such that cos(2pi/n) is an algebraic number of a 3-smooth degree, but not 2-smooth.
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14
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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; internal format)
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OFFSET
| 1,1
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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.
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MATHEMATICA
| Do[If[Take[FactorInteger[EulerPhi[2n+1]][[ -1]], 1]=={3}, Print[2n+1]], {n, 1, 10000}]
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CROSSREFS
| Cf. A004729, A051913, A058383, A125866-A125878.
Sequence in context: A180645 A196091 A129069 * A027692 A185720 A032487
Adjacent sequences: A125863 A125864 A125865 * A125867 A125868 A125869
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KEYWORD
| nonn
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AUTHOR
| Artur Jasinski (grafix(AT)csl.pl), Dec 13 2006
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EXTENSIONS
| Edited by Don Reble (djr(AT)nk.ca), Apr 24 2007
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