A225509 - OEIS

%I #19 Mar 28 2019 07:04:37

%S 15,55,75,91,175,247,275,715,775,1275,1435,2275,2635,3075,3355,4615,

%T 6355,6475,7975,8827,9139,10075,10675,11275,11935,13515,14555,21775,

%U 26455,28975,30415,31675,32395,43615,46075,47275,52195,59755,64255,77275,78403,81055

%N -5-Knödel numbers.

%C Extension of k-Knödel numbers to k negative, in this case equal to -5. Composite numbers n > 0 such that if 1 < a < n and gcd(n,a) = 1 then a^(n+5) = 1 mod n.

%H Amiram Eldar, <a href="/A225509/b225509.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); ListA225509:=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: ListA225509(10^6,-5);

%t Select[Range[10000], CompositeQ[#] && Divisible[# + 5, CarmichaelLambda[#]] &] (* _Amiram Eldar_, Mar 28 2019 *)

%Y Cf. A208728.

%Y Cf. A225506, A225507, A225508, 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