A089929 Algebraic degree of cot(Pi/n).

1, 2, 1, 4, 2, 6, 2, 6, 4, 10, 2, 12, 6, 8, 4, 16, 6, 18, 4, 12, 10, 22, 4, 20, 12, 18, 6, 28, 8, 30, 8, 20, 16, 24, 6, 36, 18, 24, 8, 40, 12, 42, 10, 24, 22, 46, 8, 42, 20, 32, 12, 52, 18, 40, 12, 36, 28, 58, 8, 60, 30, 36, 16, 48, 20, 66, 16, 44, 24, 70, 12

Offset: 2

Author

Eric W. Weisstein, Nov 15 2003

Keywords

• nonn
• hard
• nice

Comments

Also the algebraic degrees of the surface area and volume of an n-prism with unit edge lengths.

Links

• Jon Maiga, Table of n, a(n) for n = 1...400
• Eric Weisstein's World of Mathematics, Prism
• Eric Weisstein's World of Mathematics, Regular Polygon
• Eric Weisstein's World of Mathematics, Cotangent

Crossrefs

Cf. A055035, A113402.

Programs

Mathematica

a[n_] := Exponent[ MinimalPolynomial[ Cot[Pi/n]][x], x]; Table[ a[n], {n, 2, 52}] (* Jean-François Alcover, Oct 03 2012 *)

Formula

a(n) = A000010(n/gcd(n, 2)) (conjectured). - Jon Maiga, Sep 01 2019

Extensions

a(47) corrected and more terms added by Jon Maiga, Sep 01 2019