A093106 Numbers k such that the k-th cyclotomic polynomial evaluated at 2 (=A019320(k)) is not coprime to k.

6, 18, 20, 21, 54, 100, 110, 136, 147, 155, 156, 162, 253, 342, 486, 500, 602, 657, 812, 820, 889, 979, 1029, 1081, 1210, 1332, 1458, 2028, 2265, 2312, 2485, 2500, 2756, 3081, 3164, 3422, 3660, 3924, 4112, 4374, 4422, 4656, 4805, 5253, 5784, 5819, 6498

Offset

1,1

Comments

Also, numbers k such that the Zsigmondy number Zs(k, 2, 1) differs from the k-th cyclotomic polynomial evaluated at 2, i.e., A064078(k) differs from A019320(k).

Numbers k > 0 such that A019320(k) is not congruent to 1 mod k. These numbers are of the form k = p^j * A002326((p-1)/2), where p is an odd prime and j > 0. Then A019320(k) mod k = gcd(A019320(k), k) = A019320(k) / A064078(k) = p. - Thomas Ordowski, Oct 07 2017

Links

Jeppe Stig Nielsen, Table of n, a(n) for n = 1..51350

Mathematica

Select[Range[10000], GCD[#, Cyclotomic[#, 2]]!=1 &] (* Emmanuel Vantieghem, Nov 13 2016 *)

Prog

(PARI) isok(k) = gcd(polcyclo(k, 2), k) != 1; \\ Michel Marcus, Oct 07 2017
(PARI) upto(K)=li=List(); forprime(p=3, K*log(2)/log(K+1), r=znorder(Mod(2, p))*p; while(r<=K, listput(li, r); r*=p)); Set(li) \\ Jeppe Stig Nielsen, Sep 10 2020

Crossrefs

Cf. A093107, A093108, A093109.

Sequence in context: A371989 A045857 A074791 * A234752 A370865 A370863

Adjacent sequences: A093103 A093104 A093105 * A093107 A093108 A093109

Keyword

nonn

Author

Ralf Stephan, Mar 20 2004

Extensions

More terms from Vladeta Jovovic, Apr 03 2004

Definition corrected by Jerry Metzger, Nov 04 2009

Edited by Max Alekseyev, Oct 23 2017

Status

approved