A225511 -7-Knödel numbers.

33, 65, 245, 345, 1353, 1421, 1505, 2405, 3185, 4433, 4745, 6293, 6923, 7733, 8729, 9065, 9443, 9785, 15113, 16113, 18473, 19565, 21593, 30485, 30705, 32513, 35705, 42833, 45353, 50141, 55685, 57017, 64505, 66521, 67065, 73073, 79553, 80093, 83657, 91553, 96473

Offset

1,1

Comments

Extension of k-Knodel numbers to k negative, in this case equal to -7. Composite numbers n > 0 such that if 1 < a < n and gcd(n,a) = 1 then a^(n+7) = 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); ListA225511:=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: ListA225511(10^6, -7);

Mathematica

Select[Range[10000], CompositeQ[#] && Divisible[# + 7, CarmichaelLambda[#]] &] (* Amiram Eldar, Mar 28 2019 *)

Crossrefs

Cf. A208728.

Cf. A225506, A225507, A225508, A225509, A225510, A225512, A225513, A225514.

Sequence in context: A339908 A071595 A225707 * A248038 A032661 A256029

Adjacent sequences: A225508 A225509 A225510 * A225512 A225513 A225514

Keyword

nonn

Author

Paolo P. Lava, May 09 2013

Extensions

More terms from Amiram Eldar, Mar 28 2019

Status

approved