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A153508 Sarrus numbers A001567 that are not Carmichael numbers A002997. 9
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 (list; graph; refs; listen; history; text; internal format)
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 Carmichaels.

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

Cf. A001567, A002997.

Sequence in context: A043685 A043576 A215326 * A216170 A321868 A175736

Adjacent sequences:  A153505 A153506 A153507 * A153509 A153510 A153511

KEYWORD

nonn

AUTHOR

Artur Jasinski, Dec 28 2008

STATUS

approved

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Last modified April 16 07:59 EDT 2021. Contains 343030 sequences. (Running on oeis4.)