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

%I A093106 #41 Sep 11 2020 11:14:45
%S A093106 6,18,20,21,54,100,110,136,147,155,156,162,253,342,486,500,602,657,
%T A093106 812,820,889,979,1029,1081,1210,1332,1458,2028,2265,2312,2485,2500,
%U A093106 2756,3081,3164,3422,3660,3924,4112,4374,4422,4656,4805,5253,5784,5819,6498
%N A093106 Numbers k such that the k-th cyclotomic polynomial evaluated at 2 (=A019320(k)) is not coprime to k.
%C A093106 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).
%C A093106 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
%H A093106 Jeppe Stig Nielsen, <a href="/A093106/b093106.txt">Table of n, a(n) for n = 1..51350</a>
%t A093106 Select[Range[10000],GCD[#,Cyclotomic[#,2]]!=1 &] (* _Emmanuel Vantieghem_, Nov 13 2016 *)
%o A093106 (PARI) isok(k) = gcd(polcyclo(k, 2), k) != 1; \\ _Michel Marcus_, Oct 07 2017
%o A093106 (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
%Y A093106 Cf. A093107, A093108, A093109.
%K A093106 nonn
%O A093106 1,1
%A A093106 _Ralf Stephan_, Mar 20 2004
%E A093106 More terms from _Vladeta Jovovic_, Apr 03 2004
%E A093106 Definition corrected by _Jerry Metzger_, Nov 04 2009
%E A093106 Edited by _Max Alekseyev_, Oct 23 2017