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A225509 -5-Knödel numbers.

%I A225509 #20 Feb 16 2025 08:33:19
%S A225509 15,55,75,91,175,247,275,715,775,1275,1435,2275,2635,3075,3355,4615,
%T A225509 6355,6475,7975,8827,9139,10075,10675,11275,11935,13515,14555,21775,
%U A225509 26455,28975,30415,31675,32395,43615,46075,47275,52195,59755,64255,77275,78403,81055
%N A225509 -5-Knödel numbers.
%C A225509 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 A225509 Amiram Eldar, <a href="/A225509/b225509.txt">Table of n, a(n) for n = 1..1000</a>
%H A225509 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/KnoedelNumbers.html">Knödel Numbers</a>
%p A225509 with(numtheory); ListA225509:=proc(q,k) local a,n,ok;
%p A225509 for n from 2 to q do if not isprime(n) then ok:=1; for a from 1 to n do
%p A225509 if gcd(a,n)=1 then if (a^(n-k)-1) mod n<>0 then ok:=0; break; fi; fi;
%p A225509 od; if ok=1 then print(n); fi; fi; od; end: ListA225509(10^6,-5);
%t A225509 Select[Range[10000], CompositeQ[#] && Divisible[# + 5, CarmichaelLambda[#]] &] (* _Amiram Eldar_, Mar 28 2019 *)
%Y A225509 Cf. A208728.
%Y A225509 Cf. A225506, A225507, A225508, A225510, A225511, A225512, A225513, A225514,
%K A225509 nonn
%O A225509 1,1
%A A225509 _Paolo P. Lava_, May 09 2013
%E A225509 More terms from _Amiram Eldar_, Mar 28 2019