

A033553


3Knödel numbers or Dnumbers: numbers n > 3 such that n  k^(n2)k for all k with gcd(k, n) = 1.


13



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
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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(n2) which does not contain the terms 399/3=133 and 195/3=65.  Gary Detlefs, May 28 2014


LINKS

R. J. Mathar, Table of n, a(n) for n = 1..489
Eric Weisstein's World of Mathematics, DNumber.
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^(nk) 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, A208154A208158.
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



