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A153508
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Sarrus numbers A001567 that are not Carmichael numbers A002997.
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9
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341, 645, 1387, 1905, 2047, 2701, 3277, 4033, 4369, 4371, 4681, 5461, 7957, 8321, 8481, 10261, 11305, 12801, 13741, 13747, 13981, 14491, 15709, 16705, 18705, 18721, 19951, 23001, 23377, 25761, 30121, 30889, 31417, 31609, 31621, 33153, 34945
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OFFSET
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1,1
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COMMENTS
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A composite number n is a Fermat pseudoprime to base b if and only if b^(n-1) == 1 (mod n). Fermat pseudoprimes to base 2 are sometimes called Poulet numbers, Sarrus numbers, or frequently just pseudoprimes. For any given base pseudoprimes will contain Carmichael numbers as a subset. This sequence consists of base-2 Fermat pseudoprimes without the Carmichael numbers.
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LINKS
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MAPLE
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filter:= proc(n)
local q;
if isprime(n) then return false fi;
if 2 &^(n-1) mod n <> 1 then return false fi;
if not numtheory:-issqrfree(n) then return true fi;
for q in numtheory:-factorset(n) do
if (n-1) mod (q-1) <> 0 then return true fi;
od:
false
end proc:
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MATHEMATICA
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Select[Range[3, 35000, 2], !PrimeQ[#] && PowerMod[2, # - 1, # ] == 1 && !Divisible[# - 1, CarmichaelLambda[#]] &] (* Amiram Eldar, Jun 25 2019 *)
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PROG
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(Magma)
for n:= 3 to 1052503 by 2 do
if (IsOne(2^(n-1) mod n)
and not IsPrime(n)
and not n mod CarmichaelLambda(n) eq 1)
then n;
end if;
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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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