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%I #24 Sep 08 2022 08:45:39
%S 341,645,1387,1905,2047,2701,3277,4033,4369,4371,4681,5461,7957,8321,
%T 8481,10261,11305,12801,13741,13747,13981,14491,15709,16705,18705,
%U 18721,19951,23001,23377,25761,30121,30889,31417,31609,31621,33153,34945
%N Sarrus numbers A001567 that are not Carmichael numbers A002997.
%C 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.
%H Amiram Eldar, <a href="/A153508/b153508.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..306 from Brad Clardy)
%p filter:= proc(n)
%p local q;
%p if isprime(n) then return false fi;
%p if 2 &^(n-1) mod n <> 1 then return false fi;
%p if not numtheory:-issqrfree(n) then return true fi;
%p for q in numtheory:-factorset(n) do
%p if (n-1) mod (q-1) <> 0 then return true fi;
%p od:
%p false
%p end proc:
%p select(filter, [$1..10^5]); # _Robert Israel_, Dec 29 2014
%t Select[Range[3, 35000, 2], !PrimeQ[#] && PowerMod[2, # - 1, # ] == 1 && !Divisible[# - 1, CarmichaelLambda[#]] &] (* _Amiram Eldar_, Jun 25 2019 *)
%o (Magma)
%o for n:= 3 to 1052503 by 2 do
%o if (IsOne(2^(n-1) mod n)
%o and not IsPrime(n)
%o and not n mod CarmichaelLambda(n) eq 1)
%o then n;
%o end if;
%o end for; // _Brad Clardy_, Dec 25 2014
%Y Cf. A001567, A002997.
%K nonn
%O 1,1
%A _Artur Jasinski_, Dec 28 2008
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