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A225511
-7-Knödel numbers.
9
33, 65, 245, 345, 1353, 1421, 1505, 2405, 3185, 4433, 4745, 6293, 6923, 7733, 8729, 9065, 9443, 9785, 15113, 16113, 18473, 19565, 21593, 30485, 30705, 32513, 35705, 42833, 45353, 50141, 55685, 57017, 64505, 66521, 67065, 73073, 79553, 80093, 83657, 91553, 96473
OFFSET
1,1
COMMENTS
Extension of k-Knodel numbers to k negative, in this case equal to -7. Composite numbers n > 0 such that if 1 < a < n and gcd(n,a) = 1 then a^(n+7) = 1 mod n.
LINKS
Eric Weisstein's World of Mathematics, Knödel Numbers
MAPLE
with(numtheory); ListA225511:=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: ListA225511(10^6, -7);
MATHEMATICA
Select[Range[10000], CompositeQ[#] && Divisible[# + 7, 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