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A125875
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Odd numbers k such that cos(2*Pi/k) is an algebraic number of a 13-smooth degree, but not 11-smooth.
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2
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53, 79, 131, 157, 159, 169, 237, 265, 313, 371, 393, 395, 471, 477, 507, 521, 547, 553, 583, 655, 677, 689, 711, 785, 795, 845, 859, 869, 901, 911, 917, 937, 939, 1007, 1027, 1093, 1099, 1113, 1171, 1179, 1183, 1185, 1219, 1249, 1301, 1325, 1343
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OFFSET
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1,1
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COMMENTS
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A regular polygon of a(n) sides can be constructed if one also has an angle trisector, 5-, 7-, 11- and 13-sector.
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LINKS
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MATHEMATICA
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Do[If[Take[FactorInteger[EulerPhi[2n+1]][[ -1]], 1]=={13}, Print[2n+1]], {n, 1, 10000}]
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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