A225509 -5-Knödel numbers.

15, 55, 75, 91, 175, 247, 275, 715, 775, 1275, 1435, 2275, 2635, 3075, 3355, 4615, 6355, 6475, 7975, 8827, 9139, 10075, 10675, 11275, 11935, 13515, 14555, 21775, 26455, 28975, 30415, 31675, 32395, 43615, 46075, 47275, 52195, 59755, 64255, 77275, 78403, 81055

Offset

1,1

Comments

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.

Links

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

Eric Weisstein's World of Mathematics, Knödel Numbers

Maple

with(numtheory); ListA225509:=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: ListA225509(10^6, -5);

Mathematica

Select[Range[10000], CompositeQ[#] && Divisible[# + 5, CarmichaelLambda[#]] &] (* Amiram Eldar, Mar 28 2019 *)

Crossrefs

Cf. A208728.

Cf. A225506, A225507, A225508, A225510, A225511, A225512, A225513, A225514,

Sequence in context: A086643 A296324 A240814 * A235533 A039369 A119138

Adjacent sequences: A225506 A225507 A225508 * A225510 A225511 A225512

Keyword

nonn

Author

Paolo P. Lava, May 09 2013

Extensions

More terms from Amiram Eldar, Mar 28 2019

Status

approved