login
A225513
-9-Knödel numbers.
9
9, 15, 21, 27, 39, 63, 135, 171, 189, 195, 231, 315, 351, 513, 651, 663, 819, 855, 999, 1197, 1755, 1881, 2223, 2295, 2331, 3111, 3591, 4095, 4347, 4599, 4995, 5031, 5301, 6327, 7161, 9471, 9855, 10431, 10791, 11115, 11655, 12663, 12987, 13455, 14091, 14391
OFFSET
1,1
COMMENTS
Extension of k-Knodel numbers to k negative, in this case equal to -9. Composite numbers n > 0 such that if 1 < a < n and gcd(n,a) = 1 then a^(n+9) = 1 mod n.
LINKS
Eric Weisstein's World of Mathematics, Knödel Numbers
MAPLE
with(numtheory); ListA225513:=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: ListA225513(10^6, -9);
MATHEMATICA
Select[Range[10000], CompositeQ[#] && Divisible[# + 9, CarmichaelLambda[#]] &] (* Amiram Eldar, Mar 28 2019 *)
KEYWORD
nonn
AUTHOR
Paolo P. Lava, May 09 2013
EXTENSIONS
More terms from Amiram Eldar, Mar 28 2019
STATUS
approved