A089929 - OEIS

%I #25 Feb 16 2025 08:32:51

%S 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,

%T 30,8,20,16,24,6,36,18,24,8,40,12,42,10,24,22,46,8,42,20,32,12,52,18,

%U 40,12,36,28,58,8,60,30,36,16,48,20,66,16,44,24,70,12

%N Algebraic degree of cot(Pi/n).

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

%H Jon Maiga, <a href="/A089929/b089929.txt">Table of n, a(n) for n = 1...400</a>

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Prism.html">Prism</a>

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/RegularPolygon.html">Regular Polygon</a>

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Cotangent.html">Cotangent</a>

%F a(n) = A000010(n/gcd(n, 2)) (conjectured). - _Jon Maiga_, Sep 01 2019

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

%Y Cf. A055035, A113402.

%K nonn,hard,nice,changed

%O 2,2

%A _Eric W. Weisstein_, Nov 15 2003

%E a(47) corrected and more terms added by _Jon Maiga_, Sep 01 2019