A208154 6-Knödel numbers.

8, 10, 12, 18, 24, 30, 36, 42, 66, 72, 78, 84, 90, 102, 114, 126, 138, 168, 174, 186, 210, 222, 234, 246, 252, 258, 282, 318, 354, 366, 390, 396, 402, 426, 438, 456, 474, 498, 504, 534, 546, 582, 606, 618, 630, 642, 654, 678, 762, 786, 798, 822, 834, 894, 906

Offset: 1

Author

Paolo P. Lava, Feb 24 2012

Keywords

• nonn

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• Eric Weisstein's World of Mathematics, Knödel Numbers.

Crossrefs

Cf. A002997, A050990, A033553, A050992, A050993, A208155-A208158.

Programs

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(10000,6);

Mathematica

knodelQ[m_Integer?PrimeQ, n_Integer] := False; knodelQ[m_Integer, n_Integer] := Module[{i = n + 1}, While[i < m && (GCD[i, m] > 1 || Mod[i^(m - n), m] == 1), i++]; (i == m)]; Select[Range[1000], knodelQ[#, 6] &] (* Alonso del Arte, Feb 24 2012 *)