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

1,1

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): if k = 2 then 1, otherwise 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

Formula

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

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

Prog

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

Crossrefs

Cf. A000010, A055035, A197504.

Sequence in context: A295326 A032483 A057214 * A280082 A139269 A186299

Adjacent sequences: A196442 A196443 A196444 * A196446 A196447 A196448

Keyword

nonn,easy

Author

Artur Jasinski, Oct 15 2011

Extensions

Name made more specific by Wolfdieter Lang, Nov 06 2019

Status

approved