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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 (list; graph; refs; listen; history; text; internal format)
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

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

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 *)

CROSSREFS

Cf. A208728.

Cf. A225506, A225507, A225508, A225509, A225510, A225511, A225512, A225514.

Sequence in context: A163170 A097636 A179384 * A331662 A007962 A061254

Adjacent sequences:  A225510 A225511 A225512 * A225514 A225515 A225516

KEYWORD

nonn

AUTHOR

Paolo P. Lava, May 09 2013

EXTENSIONS

More terms from Amiram Eldar, Mar 28 2019

STATUS

approved

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Last modified September 16 21:28 EDT 2021. Contains 347473 sequences. (Running on oeis4.)