A225513 - OEIS

%I #13 Mar 28 2019 07:01:58

%S 9,15,21,27,39,63,135,171,189,195,231,315,351,513,651,663,819,855,999,

%T 1197,1755,1881,2223,2295,2331,3111,3591,4095,4347,4599,4995,5031,

%U 5301,6327,7161,9471,9855,10431,10791,11115,11655,12663,12987,13455,14091,14391

%N -9-Knödel numbers.

%C 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 Amiram Eldar, <a href="/A225513/b225513.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); ListA225513:=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: ListA225513(10^6,-9);

%t Select[Range[10000], CompositeQ[#] && Divisible[# + 9, CarmichaelLambda[#]] &] (* _Amiram Eldar_, Mar 28 2019 *)

%Y Cf. A208728.

%Y Cf. A225506, A225507, A225508, A225509, A225510, A225511, A225512, A225514.

%K nonn

%O 1,1

%A _Paolo P. Lava_, May 09 2013

%E More terms from _Amiram Eldar_, Mar 28 2019