A225508 - OEIS

%I #17 Mar 28 2019 07:04:51

%S 4,6,8,12,14,16,20,24,40,48,56,60,66,80,104,120,140,176,204,240,260,

%T 266,476,560,696,728,920,1020,1040,1292,1508,1634,1736,1820,1976,2320,

%U 2544,2660,3416,3440,3848,4136,4686,4756,5180,5456,6188,6608,7280,8004,8816

%N -4-Knödel numbers.

%C Extension of k-Knödel numbers to k negative, in this case equal to -4. Composite numbers n > 0 such that if 1 < a < n and gcd(n,a) = 1 then a^(n+4) = 1 mod n.

%C All terms are even numbers.

%H Amiram Eldar, <a href="/A225508/b225508.txt">Table of n, a(n) for n = 1..1000</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/KnoedelNumbers.html">Knödel Numbers</a>

%p with(numtheory); ListA225508:=proc(q,k) local a,n,ok;

%p for n from 2 to q do if not isprime(n) then ok:=1; for a from 1 to n do

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

%p od; if ok=1 then print(n); fi; fi; od; end: ListA225508(10^6,-4);

%t Select[Range[10000], CompositeQ[#] && Divisible[# + 4, CarmichaelLambda[#]] &] (* _Amiram Eldar_, Mar 28 2019 *)

%Y Cf. A208728.

%Y Cf. A225506, A225507, A225509, A225510, A225511, A225512, A225513, A225514.

%K nonn

%O 1,1

%A _Paolo P. Lava_, May 09 2013

%E More terms from _Amiram Eldar_, Mar 28 2019