This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A366900 #24 Dec 12 2023 10:31:45 %S A366900 0,0,1,0,1,1,1,0,1,1,1,2,1,1,3,0,1,1,1,2,3,1,1,2,1,1,1,2,1,3,1,0,3,1, %T A366900 3,2,1,1,3,2,1,3,1,2,3,1,1,2,1,1,3,2,1,1,3,2,3,1,1,4,1,1,3,0,3,3,1,2, %U A366900 3,3,1,2,1,1,3,2,3,3,1,2,1,1,1,4,3,1,3 %N A366900 a(n) is the number of real roots of the derivative of the cyclotomic polynomial Phi(n, 1/x). %F A366900 For n = 2^m, a(n) = 0; %F A366900 For odd n = p^m, a(n) = 1; %F A366900 For odd n = p1^r1*p2^r2*...*pm^rm, a(n) = 2m-1; %F A366900 For n = 2*p1^r1*p2^r2*...*pm^rm, a(n) = 2m-1 if p1, ..., pm are odd; %F A366900 For n = 2^r*p1^r1*p2^r2*...*pm^rm, a(n) = 2m if p1, ..., pm are odd and r > 1. %t A366900 c[n_, y_] := Limit[D[Cyclotomic[n, 1/x], x], x -> y]; Table[Length[Solve[c[n, x] == 0, x, Reals]], {n, 1, 128}] %o A366900 (PARI) a(n)=my(v=valuation(n,2)); 2*omega(n>>v) - (v <= 1 && n > 2) \\ _Andrew Howroyd_, Oct 27 2023 %K A366900 nonn %O A366900 1,12 %A A366900 _Gevorg Hmayakyan_, Oct 26 2023