OFFSET
1,1
COMMENTS
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.
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..306 from Brad Clardy)
MAPLE
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:
select(filter, [$1..10^5]); # Robert Israel, Dec 29 2014
MATHEMATICA
Select[Range[3, 35000, 2], !PrimeQ[#] && PowerMod[2, # - 1, # ] == 1 && !Divisible[# - 1, CarmichaelLambda[#]] &] (* Amiram Eldar, Jun 25 2019 *)
PROG
(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;
end for; // Brad Clardy, Dec 25 2014
CROSSREFS
KEYWORD
nonn
AUTHOR
Artur Jasinski, Dec 28 2008
STATUS
approved