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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

Amiram Eldar, Table of n, a(n) for n = 1..1000

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.

Cf. A225506, A225508, A225509, A225510, A225511, A225512, A225513, A225514.

Sequence in context: A020137 A231570 A020190 * A135187 A246318 A277715

Adjacent sequences:  A225504 A225505 A225506 * A225508 A225509 A225510

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 June 20 11:38 EDT 2019. Contains 324234 sequences. (Running on oeis4.)