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A225507
-3-Knödel numbers.
9
9, 21, 45, 63, 105, 117, 273, 285, 585, 627, 765, 1365, 1449, 1677, 3705, 3885, 4221, 4485, 4797, 7137, 7565, 8109, 10197, 10545, 11445, 13065, 14637, 16965, 19437, 20805, 26061, 27645, 30573, 31317, 33705, 35853, 38805, 39897, 40887, 41181, 48633, 50505, 57057
OFFSET
1,1
COMMENTS
Extension of k-Knödel numbers to k negative, in this case equal to -3. Composite numbers n > 0 such that if 1 < a < n and gcd(n,a) = 1 then a^(n+3) = 1 mod n.
LINKS
Eric Weisstein's World of Mathematics, Knödel Numbers
MAPLE
with(numtheory); ListA225507:=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: ListA225507(10^6, -3);
MATHEMATICA
Select[Range[10000], CompositeQ[#] && Divisible[# + 3, CarmichaelLambda[#]] &] (* Amiram Eldar, Mar 28 2019 *)
KEYWORD
nonn
AUTHOR
Paolo P. Lava, May 09 2013
EXTENSIONS
Incorrect comment deleted by Joseph DeVincentis, Dec 04 2015
More terms from Amiram Eldar, Mar 28 2019
STATUS
approved