

A196445


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


2



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
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OFFSET

1,1


COMMENTS

All numbers in this sequence are even integers. For A196445/2 see A197504.
All these cases are socalled 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


LINKS

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


FORMULA

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


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


CROSSREFS

Cf. 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



