A093107 -id:A093107 - cp's OEIS frontend

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

Ralf Stephan, Mar 20 2004

nonn

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

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

Cf. A093107, A093108, A093109.

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

isok(k) = gcd(polcyclo(k, 2), k) != 1; \\ Michel Marcus, Oct 07 2017

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

More terms from Vladeta Jovovic, Apr 03 2004
Definition corrected by Jerry Metzger, Nov 04 2009
Edited by Max Alekseyev, Oct 23 2017

A093108 Numbers n such that the Zsigmondy number Zs(n,4,1) differs from the n-th cyclotomic polynomial evaluated at 4.

Original entry on oeis.org

3, 9, 10, 21, 27, 50, 55, 68, 78, 81, 147, 155, 171, 243, 250, 253, 301, 406, 410, 605, 657, 666, 729, 889, 979, 1014, 1029, 1081, 1156, 1250, 1378, 1582, 1711, 1830, 1962, 2056, 2187, 2211, 2265, 2328, 2485, 2892, 3081, 3249, 3403, 4082, 4658, 4805, 4965

Offset: 1

Ralf Stephan, Mar 20 2004

nonn

A019322(n) does not equal A064080(n).

Cf. A093107, A093106, A093109.

Select[Range[10000], GCD[#, Cyclotomic[#, 4]]!=1 &] (* Emmanuel Vantieghem, Nov 13 2016 *)

More terms from Vladeta Jovovic, Apr 02 2004

Definition corrected by Jerry Metzger, Nov 04 2009

A093109 Numbers n such that the Zsigmondy number Zs(n,5,1) differs from the n-th cyclotomic polynomial evaluated at 5.

Original entry on oeis.org

2, 4, 6, 8, 16, 18, 32, 42, 52, 54, 55, 64, 93, 128, 162, 171, 256, 272, 294, 355, 406, 486, 506, 512, 605, 676, 820, 1024, 1332, 1458, 1474, 1711, 1806, 1830, 2048, 2058, 2162, 2504, 2525, 2715, 2756, 2883, 2943, 3081, 3249, 3629, 3916, 4096, 4374, 4624, 5210

Offset: 1

Ralf Stephan, Mar 20 2004

nonn

Numbers n such that A019323(n) does not equal A064081(n).
Vladeta Jovovic points out that the sequence seems to contain the powers of two as well as the numbers of the form 2*3^k.
Numbers of the form ord(5,p)*p^k where prime p <> 5 and k > 0. Also numbers n > 0 such that A019323(n) =/= 1 (mod n). Also A019323(n) mod n = gcd(n, A019323(n)) = p. - Thomas Ordowski, Oct 22 2017

Cf. A093106, A093107, A093108, A019323, A064081.

Select[Range[10000], GCD[#, Cyclotomic[#, 5]]!=1 &] (* Emmanuel Vantieghem, Nov 13 2016 *)

More terms from Vladeta Jovovic, Apr 02 2004

Definition corrected by Jerry Metzger, Nov 04 2009

cp's OEIS Frontend

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

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A093108 Numbers n such that the Zsigmondy number Zs(n,4,1) differs from the n-th cyclotomic polynomial evaluated at 4.

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A093109 Numbers n such that the Zsigmondy number Zs(n,5,1) differs from the n-th cyclotomic polynomial evaluated at 5.

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