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A084653 Pseudoprimes whose prime factors do not divide any smaller pseudoprime. 8
341, 1387, 2047, 8321, 13747, 18721, 19951, 31621, 60701, 83333, 88357, 219781, 275887, 422659, 435671, 513629, 514447, 587861, 604117, 653333, 680627, 710533, 722261, 741751, 769757, 916327, 1194649, 1252697, 1293337, 1433407, 1441091 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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).

LINKS

T. D. Noe, Table of n, a(n) for n = 1..10000

R. G. E. Pinch, Pseudoprimes and their factors (FTP)

Eric Weisstein's World of Mathematics, Pseudoprime

Index entries for sequences related to pseudoprimes

EXAMPLE

a(2) = 1387 because 1387 = 19*73 and the smaller pseudoprimes (341, 561, 645, 1105) do not have the factors 19 or 73.

CROSSREFS

Cf. A001220, A001567, A084654, A084655.

Sequence in context: A086837 A020230 A087716 * A143688 A086250 A285549

Adjacent sequences:  A084650 A084651 A084652 * A084654 A084655 A084656

KEYWORD

nonn

AUTHOR

T. D. Noe, Jun 02 2003

STATUS

approved

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