A050990 2-Knödel numbers.

4, 6, 8, 10, 12, 14, 22, 24, 26, 30, 34, 38, 46, 56, 58, 62, 74, 82, 86, 94, 106, 118, 122, 132, 134, 142, 146, 158, 166, 178, 182, 194, 202, 206, 214, 218, 226, 254, 262, 274, 278, 298, 302, 314, 326, 334, 346, 358, 362, 382, 386, 394, 398, 422, 446, 454, 458

Offset: 1

Author

Eric W. Weisstein

Keywords

• nonn

Comments

Numbers k > 2 such that A002322(k) divides k-2. Contains all doubled primes and all doubled Carmichael numbers. - Thomas Ordowski, Apr 23 2017

Problem: are there infinitely many 2-Knodel numbers divisible by 4? - Thomas Ordowski, Jun 21 2017

Named after the Austrian mathematician and computer scientist Walter Knödel (1926-2018). - Amiram Eldar, Jun 08 2021

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000 (first 690 terms from R. J. Mathar)
• John H. Castillo and Jhony Fernando Caranguay Mainguez, The set of k-units modulo n, arXiv:1708.06812 [math.NT], 2017.
• Eric Weisstein's World of Mathematics, Knödel Numbers.
• Wikipedia, Knödel number.

Crossrefs

Cf. A002997, A033553, A050992, A050993, A208154, A208155, A208156, A208157, A208158.

Programs

Mathematica

Select[Range[4, 460, 2], Divisible[# - 2, CarmichaelLambda@ #] &] (* Michael De Vlieger, Apr 24 2017 *)

PARI

a002322(n) = lcm(znstar(n)[2]);
forstep(n=4, 500, 2, if((n - 2)%a002322(n)==0, print1(n,", "))) \\ Indranil Ghosh, Jun 22 2017