Search: id:A084653
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%I A084653
%S A084653 341,1387,2047,8321,13747,18721,19951,31621,60701,83333,88357,219781,
%T A084653 275887,422659,435671,513629,514447,587861,604117,653333,680627,710533,
%U A084653 722261,741751,769757,916327,1194649,1252697,1293337,1433407,1441091
%N A084653 Pseudoprimes whose prime factors do not divide any smaller pseudoprime.
%C A084653 Here pseudoprime means a Fermat base-2 pseudoprime; sequence A001567, 
               a composite number n such that n divides 2^(n-1) - 1. All numbers 
               in this sequence seem to have only two prime factors - a conjecture 
               that has been tested for all pseudoprimes < 10^15. The two prime 
               factors are given in A084654 and A084655. The two prime factors are 
               the same when the pseudoprime is the square of a Wieferich prime 
               (A001220).
%H A084653 R. G. E. Pinch, <a href="ftp://ftp.dpmms.cam.ac.uk/pub/PSP/">Pseudoprimes 
               and their factors (FTP)</a>
%H A084653 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               Pseudoprime.html">Pseudoprime</a>
%e A084653 a(2) = 1387 because 1387 = 19*73 and the smaller pseudoprimes (341, 561, 
               645, 1105) do not have the factors 19 or 73.
%Y A084653 Cf. A001220, A001567, A084654, A084655.
%Y A084653 Sequence in context: A086837 A020230 A087716 this_sequence A143688 A086250 
               A069309
%Y A084653 Adjacent sequences: A084650 A084651 A084652 this_sequence A084654 A084655 
               A084656
%K A084653 nonn
%O A084653 1,1
%A A084653 T. D. Noe (noe(AT)sspectra.com), Jun 02 2003

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