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%I #7 Apr 12 2012 15:11:41
%S 341,1387,2047,8321,13747,18721,19951,31621,60701,83333,88357,219781,
%T 275887,422659,435671,513629,514447,587861,604117,653333,680627,
%U 710533,722261,741751,769757,916327,1194649,1252697,1293337,1433407,1441091
%N Pseudoprimes whose prime factors do not divide any smaller pseudoprime.
%C 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 T. D. Noe, <a href="/A084653/b084653.txt">Table of n, a(n) for n = 1..10000</a>
%H R. G. E. Pinch, <a href="ftp://ftp.dpmms.cam.ac.uk/pub/PSP/">Pseudoprimes and their factors (FTP)</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Pseudoprime.html">Pseudoprime</a>
%H <a href="/index/Ps#pseudoprimes">Index entries for sequences related to pseudoprimes</a>
%e a(2) = 1387 because 1387 = 19*73 and the smaller pseudoprimes (341, 561, 645, 1105) do not have the factors 19 or 73.
%Y Cf. A001220, A001567, A084654, A084655.
%K nonn
%O 1,1
%A _T. D. Noe_, Jun 02 2003
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