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
KEYWORD
nonn
AUTHOR
Paolo P. Lava, May 09 2013
EXTENSIONS
More terms from Rémy Sigrist, Mar 03 2019
STATUS
approved