A084653 Pseudoprimes whose prime factors do not divide any smaller pseudoprime.

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

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 * A354694 A143688 A086250

Adjacent sequences: A084650 A084651 A084652 * A084654 A084655 A084656

Keyword

nonn

Author

T. D. Noe, Jun 02 2003

Status

approved