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

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

Author

Ralf Stephan, Mar 20 2004

Keywords

• nonn

Comments

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

Crossrefs

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

Programs

Mathematica

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

Extensions

More terms from Vladeta Jovovic, Apr 02 2004

Definition corrected by Jerry Metzger, Nov 04 2009