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A033553 3-Knodel numbers or D-numbers: numbers n > 3 such that n | k^(n-2)-k for all k with gcd(k, n) = 1. 11
9, 15, 21, 33, 39, 51, 57, 63, 69, 87, 93, 111, 123, 129, 141, 159, 177, 183, 195, 201, 213, 219, 237, 249, 267, 291, 303, 309, 315, 321, 327, 339, 381, 393, 399, 411, 417, 447, 453, 471, 489, 501, 519, 537, 543, 573, 579, 591, 597, 633, 669, 681, 687, 693 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

All terms are divisible by 3.  All terms satisfy the condition 2^n == 8 (mod n). The only number less than 693 which satisfies this condition and is not listed is 248, which is not divisible by 3. a(n)/3 is nearly identical to A106317(n-2) which does not contain the terms 399/3=133 and 195/3=65. - Gary Detlefs, May 28 2014

LINKS

Table of n, a(n) for n=1..54.

Eric Weisstein's World of Mathematics, D-Number.

Eric Weisstein's World of Mathematics, Knoedel 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, 3) # Paolo P. Lava, Feb 24 2012

CROSSREFS

Cf. A002997, A050990, A050992, A050993, A208154-A208158.

Sequence in context: A175626 A096788 A050991 * A020192 A241809 A063174

Adjacent sequences:  A033550 A033551 A033552 * A033554 A033555 A033556

KEYWORD

nonn

AUTHOR

David W. Wilson

EXTENSIONS

Edited by N. J. A. Sloane, May 07 2007

STATUS

approved

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Last modified November 29 01:24 EST 2014. Contains 250479 sequences.