A196445 Numbers k >= 2 such that A055035(k) is an odd integer.

2, 6, 14, 18, 22, 38, 46, 54, 62, 86, 94, 98, 118, 134, 142, 158, 162, 166, 206, 214, 242, 254, 262, 278, 302, 326, 334, 358, 382, 398, 422, 446, 454, 478, 486, 502, 526, 542, 566, 614, 622, 662, 686, 694, 718, 722, 734, 758, 766, 838, 862, 878, 886, 926, 934, 958, 974, 982, 998

Offset: 1

Author

Artur Jasinski, Oct 15 2011

Keywords

• nonn
• easy

Comments

All terms are even.

All these cases are so-called reversed cases when degree of minimal polynomial of cos(Pi/n) = 2*degree of minimal polynomial of sin(Pi/n) (in rest of cases is vice versa).

For k = 1, A055035(1) = 1 is also odd. - Wolfdieter Lang, Nov 06 2019

The elements of the set {k == 2 (mod 4): k = 2 or phi(k/2)/2 is odd} sorted increasingly, where phi = A000010 (Euler's totient). - Wolfdieter Lang, Nov 06 2019

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000010, A055035, A197504.

Programs

Mathematica

a[n_] := If[n == 2, 1, EulerPhi[n]/{1, 1, 2, 1}[[Mod[n, 4] + 1]]]; aa = {}; Do[If[OddQ[a[n]], AppendTo[aa, n]], {n, 2, 1000}]; aa

PARI

isok(k) = ((k%4) == 2) && ((k==2) || (eulerphi(k/2)/2 % 2)==1); \\ after Wolfdieter Lang comment; Michel Marcus, Jan 29 2023

Formula

a(n) = 2*A197504(n).

Extensions

Name made more specific by Wolfdieter Lang, Nov 06 2019