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A225513 -9-Knödel numbers.

%I A225513 #14 Feb 16 2025 08:33:19
%S A225513 9,15,21,27,39,63,135,171,189,195,231,315,351,513,651,663,819,855,999,
%T A225513 1197,1755,1881,2223,2295,2331,3111,3591,4095,4347,4599,4995,5031,
%U A225513 5301,6327,7161,9471,9855,10431,10791,11115,11655,12663,12987,13455,14091,14391
%N A225513 -9-Knödel numbers.
%C A225513 Extension of k-Knodel numbers to k negative, in this case equal to -9. Composite numbers n > 0 such that if 1 < a < n and gcd(n,a) = 1 then a^(n+9) = 1 mod n.
%H A225513 Amiram Eldar, <a href="/A225513/b225513.txt">Table of n, a(n) for n = 1..1000</a>
%H A225513 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/KnoedelNumbers.html">Knödel Numbers</a>
%p A225513 with(numtheory); ListA225513:=proc(q,k) local a,n,ok;
%p A225513 for n from 2 to q do if not isprime(n) then ok:=1; for a from 1 to n do
%p A225513 if gcd(a,n)=1 then if (a^(n-k)-1) mod n<>0 then ok:=0; break; fi; fi;
%p A225513 od; if ok=1 then print(n); fi; fi; od; end: ListA225513(10^6,-9);
%t A225513 Select[Range[10000], CompositeQ[#] && Divisible[# + 9, CarmichaelLambda[#]] &] (* _Amiram Eldar_, Mar 28 2019 *)
%Y A225513 Cf. A208728.
%Y A225513 Cf. A225506, A225507, A225508, A225509, A225510, A225511, A225512, A225514.
%K A225513 nonn
%O A225513 1,1
%A A225513 _Paolo P. Lava_, May 09 2013
%E A225513 More terms from _Amiram Eldar_, Mar 28 2019