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Search: id:A125866
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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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+0
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; listen)
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OFFSET
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1,1
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COMMENT
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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
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Do[If[Take[FactorInteger[EulerPhi[2n+1]][[ -1]], 1]=={3}, Print[2n+1]], {n, 1, 10000}]
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CROSSREFS
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Cf. A004729, A051913, A058383, A125866-A125878.
Sequence in context: A067020 A051913 A129069 this_sequence A027692 A032487 A063189
Adjacent sequences: A125863 A125864 A125865 this_sequence A125867 A125868 A125869
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KEYWORD
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nonn
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AUTHOR
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Artur Jasinski (grafix(AT)csl.pl), Dec 13 2006
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EXTENSIONS
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Edited by Don Reble (djr(AT)nk.ca), Apr 24 2007
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