A225513 -9-Knödel numbers.

9, 15, 21, 27, 39, 63, 135, 171, 189, 195, 231, 315, 351, 513, 651, 663, 819, 855, 999, 1197, 1755, 1881, 2223, 2295, 2331, 3111, 3591, 4095, 4347, 4599, 4995, 5031, 5301, 6327, 7161, 9471, 9855, 10431, 10791, 11115, 11655, 12663, 12987, 13455, 14091, 14391

Offset

1,1

Comments

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.

Links

Amiram Eldar, Table of n, a(n) for n = 1..1000

Eric Weisstein's World of Mathematics, Knödel Numbers

Maple

with(numtheory); ListA225513:=proc(q, k) local a, n, ok;
for n from 2 to q do if not isprime(n) then ok:=1; for a from 1 to n do
if gcd(a, n)=1 then if (a^(n-k)-1) mod n<>0 then ok:=0; break; fi; fi;
od; if ok=1 then print(n); fi; fi; od; end: ListA225513(10^6, -9);

Mathematica

Select[Range[10000], CompositeQ[#] && Divisible[# + 9, CarmichaelLambda[#]] &] (* Amiram Eldar, Mar 28 2019 *)

Crossrefs

Cf. A208728.

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

Sequence in context: A163170 A097636 A179384 * A331662 A007962 A061254

Adjacent sequences: A225510 A225511 A225512 * A225514 A225515 A225516

Keyword

nonn

Author

Paolo P. Lava, May 09 2013

Extensions

More terms from Amiram Eldar, Mar 28 2019

Status

approved