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A225510 -6-Knödel numbers.

%I A225510 #15 Feb 16 2025 08:33:19
%S A225510 4,6,8,10,12,18,24,30,36,42,44,72,78,84,90,126,168,170,210,228,234,
%T A225510 252,264,390,504,546,570,630,714,744,924,1110,1170,1254,1530,1548,
%U A225510 1596,1638,2262,2574,2604,2730,2898,3354,3978,3990,4674,5544,5688,6204,7254,7410
%N A225510 -6-Knödel numbers.
%C A225510 Extension of k-Knodel numbers to k negative, in this case equal to -6. Composite numbers n > 0 such that if 1 < a < n and gcd(n,a) = 1 then a^(n+6) = 1 mod n.
%H A225510 Amiram Eldar, <a href="/A225510/b225510.txt">Table of n, a(n) for n = 1..1000</a>
%H A225510 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/KnoedelNumbers.html">Knödel Numbers</a>
%p A225510 with(numtheory); ListA225510:=proc(q,k) local a,n,ok;
%p A225510 for n from 2 to q do if not isprime(n) then ok:=1; for a from 1 to n do
%p A225510 if gcd(a,n)=1 then if (a^(n-k)-1) mod n<>0 then ok:=0; break; fi; fi;
%p A225510 od; if ok=1 then print(n); fi; fi; od; end: ListA225510(10^6,-6);
%t A225510 Select[Range[10000], CompositeQ[#] && Divisible[# + 6, CarmichaelLambda[#]] &] (* _Amiram Eldar_, Mar 28 2019 *)
%Y A225510 Cf. A208728.
%Y A225510 Cf. A225506, A225507, A225508, A225509, A225511, A225512, A225513, A225514.
%K A225510 nonn
%O A225510 1,1
%A A225510 _Paolo P. Lava_, May 09 2013