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A055035
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Degree of minimal polynomial of sin(pi/n) over the rationals.
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3
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1, 1, 2, 2, 4, 1, 6, 4, 6, 2, 10, 4, 12, 3, 8, 8, 16, 3, 18, 8, 12, 5, 22, 8, 20, 6, 18, 12, 28, 4, 30, 16, 20, 8, 24, 12, 36, 9, 24, 16, 40, 6, 42, 20, 24, 11, 46, 16, 42, 10, 32, 24, 52, 9, 40, 24, 36, 14, 58, 16, 60, 15, 36, 32, 48, 10, 66, 32, 44, 12, 70, 24, 72
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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COMMENTS
| Also degree of minimal polynomial of function F(n)=(gamma(1/n)*gamma((n-1)/n))/pi over the rationals. Roots of minimal polynomials of F(n) belonging to algebraic extension of sin(n/Pi) and vice versa (e.g. gamma(1/11)*gamma(10/11)/pi = 20*sin(pi/11) - 112*sin(pi/11)^3 + 256*sin(pi/11)^5 - 256*sin(pi/11)^7 + (1024*sin(pi/11)^9)/11). (* Artur Jasinski, Oct 17 2011 *)
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LINKS
| Eric Weisstein's World of Mathematics, Trigonometry Angles
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FORMULA
| a(1)=1, a(2)=1, a(n)=phi(n)/(1, 1, 2, 1 for n=0, 1, 2, 3 mod 4) for n>2,
where phi is Euler's totient, A000010.
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MATHEMATICA
| a[n_] := If[n==2, 1, EulerPhi[n]/{1, 1, 2, 1}[[Mod[n, 4]+1]]]; Table[a[n], {n, 80}]
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CROSSREFS
| Cf. A000010.
Sequence in context: A072211 A070306 A014665 * A204595 A173897 A152593
Adjacent sequences: A055032 A055033 A055034 * A055036 A055037 A055038
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KEYWORD
| easy,nonn
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AUTHOR
| Shawn Cokus (Cokus(AT)math.washington.edu)
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