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A225510
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-6-Knödel numbers.
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9
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4, 6, 8, 10, 12, 18, 24, 30, 36, 42, 44, 72, 78, 84, 90, 126, 168, 170, 210, 228, 234, 252, 264, 390, 504, 546, 570, 630, 714, 744, 924, 1110, 1170, 1254, 1530, 1548, 1596, 1638, 2262, 2574, 2604, 2730, 2898, 3354, 3978, 3990, 4674, 5544, 5688, 6204, 7254, 7410
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OFFSET
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1,1
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COMMENTS
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Extension of k-Knodel numbers to k negative, in this case equal to -6. Composite numbers n > 0 such that if 1 < a < n and gcd(n,a) = 1 then a^(n+6) = 1 mod n.
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LINKS
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MAPLE
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with(numtheory); ListA225510:=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: ListA225510(10^6, -6);
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MATHEMATICA
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Select[Range[10000], CompositeQ[#] && Divisible[# + 6, CarmichaelLambda[#]] &] (* Amiram Eldar, Mar 28 2019 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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