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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 (list; graph; refs; listen; history; text; internal format)
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 *)
CROSSREFS
Cf. A208728.
Sequence in context: A020137 A231570 A020190 * A135187 A246318 A277715
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

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Last modified March 29 07:27 EDT 2024. Contains 371265 sequences. (Running on oeis4.)