A225512 -8-Knödel numbers.

4, 6, 8, 12, 16, 20, 22, 24, 28, 32, 40, 48, 52, 60, 80, 96, 112, 120, 132, 136, 160, 208, 240, 280, 322, 352, 364, 408, 480, 520, 532, 580, 680, 682, 952, 1036, 1120, 1312, 1392, 1456, 1612, 1768, 1840, 2040, 2080, 2332, 2584, 3016, 3172, 3268, 3472, 3640

Offset

1,1

Comments

Extension of k-Knodel numbers to k negative, in this case equal to -8. Composite numbers n > 0 such that if 1 < a < n and gcd(n,a) = 1 then a^(n+8) = 1 mod n.

Links

Rémy Sigrist, Table of n, a(n) for n = 1..1000

Eric Weisstein's World of Mathematics, Knödel Numbers

Maple

with(numtheory); ListA225512:=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: ListA225512(10^6, -8);

Mathematica

Select[Range[10000], CompositeQ[#] && Divisible[# + 8, CarmichaelLambda[#]] &] (* Amiram Eldar, Mar 28 2019 *)

Prog

(PARI) is(n) = if (bigomega(n)>1, for (a=2, n-1, if (gcd(n, a)==1 && Mod(a, n)^(n+8)!=1, return (0))); return (1), return (0)) \\ Rémy Sigrist, Mar 03 2019

Crossrefs

Cf. A208728.

Cf. A225506, A225507, A225508, A225509, A225510, A225511, A225513, A225514.

Sequence in context: A113709 A076082 A162648 * A233036 A062554 A020225

Adjacent sequences: A225509 A225510 A225511 * A225513 A225514 A225515

Keyword

nonn

Author

Paolo P. Lava, May 09 2013

Extensions

More terms from Rémy Sigrist, Mar 03 2019

Status

approved