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A225512
-8-Knödel numbers.
9
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
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
KEYWORD
nonn
AUTHOR
Paolo P. Lava, May 09 2013
EXTENSIONS
More terms from Rémy Sigrist, Mar 03 2019
STATUS
approved