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A093819
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Algebraic degree of Sin[2Pi/n].
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4
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1, 1, 2, 1, 4, 2, 6, 2, 6, 4, 10, 1, 12, 6, 8, 4, 16, 6, 18, 2, 12, 10, 22, 4, 20, 12, 18, 3, 28, 8, 30, 8, 20, 16, 24, 3, 36, 18, 24, 8, 40, 12, 42, 5, 24, 22, 46, 8, 42, 20, 32, 6, 52, 18, 40, 12, 36, 28, 58, 4, 60, 30, 36, 16, 48, 20, 66, 8, 44, 24, 70, 12, 72, 36, 40, 9, 60, 24
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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COMMENTS
| The degree formula given in the I. Niven reference on p. 37-8 (see below) appears as part of theorem 3.9 attributed to D. H. Lehmer. However, this part, concerning Sin[2Pi/n], differs from Lehmer's result, which in fact is incorrect. [From Wolfdieter Lang, Jan 09 2011.]
This is also the algebraic degree of the area of a regular n-gon inscribed in the unit circle. [From Jack Grahl (j.grahl(AT)ucl.ac.uk), Jan 10 2011]
Every degree appears in this sequence except for the half-nontotients, A079695. [T. D. Noe, Jan 12 2011]
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REFERENCES
| I. Niven, Irrational Numbers, The Math. Assoc. of America, second printing, 1963, distributed by John Wiley and Sons.
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LINKS
| Eric Weisstein's World of Mathematics, Trigonometry Angles
T. D. Noe, Table of n, a(n) for n = 1..1000
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FORMULA
| a(4)=1, a(n)=phi(n) if gcd(n,8)<4; a(n)=phi(n)/4 if gcd(n,8)=4, and a(n)=phi(n)/2 if gcd(n,8)>4. Here phi(n)=A000010(n) (Euler totient). See the I. Niven reference, Theorem 3.9, p. 37-8. W. Lang, Jan 09 2011.
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MATHEMATICA
| a[4]=1; a[n_] := Module[{g=GCD[n, 8], e=EulerPhi[n]}, If[g<4, e, If[g==4, e/4, e/2]]]; Array[a, 1000]
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CROSSREFS
| Cf. A055035, A023022 (alg. degree of Cos[2Pi/n]), A183919.
Sequence in context: A175542 A076686 A114810 * A089929 A131888 A109170
Adjacent sequences: A093816 A093817 A093818 * A093820 A093821 A093822
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KEYWORD
| nonn
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AUTHOR
| Eric Weisstein (eric(AT)weisstein.com), Apr 16, 2004
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