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A050990 2-Knödel numbers. 14
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

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

LINKS

R. J. Mathar, Table of n, a(n) for n = 1..690

Eric Weisstein's World of Mathematics, Knödel Numbers.

MAPLE

with(numtheory);

knodel:=proc(i, k)

local a, n, ok;

for n from k+1 to i do

  ok:=1;

  for a from 1 to n do

     if gcd(a, n)=1 then  if (a^(n-k) mod n)<>1 then ok:=0; break; fi; fi;

  od;

  if ok=1 then print(n); fi;

od;

end:

knodel(1000, 2) # Paolo P. Lava, Feb 24 2012

MATHEMATICA

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

PROG

(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

CROSSREFS

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

Sequence in context: A061344 A066664 A064938 * A289425 A225514 A161546

Adjacent sequences:  A050987 A050988 A050989 * A050991 A050992 A050993

KEYWORD

nonn

AUTHOR

Eric W. Weisstein

STATUS

approved

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Last modified August 23 19:47 EDT 2017. Contains 291021 sequences.