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

Author

Paolo P. Lava, May 09 2013

Keywords

• nonn

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

Crossrefs

Cf. A208728.

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

Programs

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 *)

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

Extensions

More terms from Rémy Sigrist, Mar 03 2019