A225508 -4-Knödel numbers.

4, 6, 8, 12, 14, 16, 20, 24, 40, 48, 56, 60, 66, 80, 104, 120, 140, 176, 204, 240, 260, 266, 476, 560, 696, 728, 920, 1020, 1040, 1292, 1508, 1634, 1736, 1820, 1976, 2320, 2544, 2660, 3416, 3440, 3848, 4136, 4686, 4756, 5180, 5456, 6188, 6608, 7280, 8004, 8816

Offset

1,1

Comments

Extension of k-Knödel numbers to k negative, in this case equal to -4. Composite numbers n > 0 such that if 1 < a < n and gcd(n,a) = 1 then a^(n+4) = 1 mod n.

All terms are even numbers.

Links

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

Eric Weisstein's World of Mathematics, Knödel Numbers

Maple

with(numtheory); ListA225508:=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: ListA225508(10^6, -4);

Mathematica

Select[Range[10000], CompositeQ[#] && Divisible[# + 4, CarmichaelLambda[#]] &] (* Amiram Eldar, Mar 28 2019 *)

Crossrefs

Cf. A208728.

Cf. A225506, A225507, A225509, A225510, A225511, A225512, A225513, A225514.

Sequence in context: A047407 A090697 A359675 * A235036 A107303 A028876

Adjacent sequences: A225505 A225506 A225507 * A225509 A225510 A225511

Keyword

nonn

Author

Paolo P. Lava, May 09 2013

Extensions

More terms from Amiram Eldar, Mar 28 2019

Status

approved