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

Author

T. D. Noe, Jun 02 2003

Keywords

• nonn

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).

Examples

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

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

Crossrefs

Cf. A001220, A001567, A084654, A084655.