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Search: id:A084653
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| A084653 |
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Pseudoprimes whose prime factors do not divide any smaller pseudoprime. |
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+0
7
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| 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; listen)
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OFFSET
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1,1
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COMMENT
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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).
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LINKS
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R. G. E. Pinch, Pseudoprimes and their factors (FTP)
Eric Weisstein's World of Mathematics, Pseudoprime
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EXAMPLE
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a(2) = 1387 because 1387 = 19*73 and the smaller pseudoprimes (341, 561, 645, 1105) do not have the factors 19 or 73.
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CROSSREFS
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Cf. A001220, A001567, A084654, A084655.
Sequence in context: A086837 A020230 A087716 this_sequence A143688 A086250 A069309
Adjacent sequences: A084650 A084651 A084652 this_sequence A084654 A084655 A084656
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KEYWORD
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nonn
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AUTHOR
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T. D. Noe (noe(AT)sspectra.com), Jun 02 2003
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