A084655 -id:A084655 - cp's OEIS frontend

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

T. D. Noe, Jun 02 2003

nonn

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).

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

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

Cf. A001220, A001567, A084654, A084655.

A242276 Irregular array of factors of n-th Poulet number read by rows, where row n corresponds to A001567(n).

Original entry on oeis.org

11, 31, 3, 11, 17, 3, 5, 43, 5, 13, 17, 19, 73, 7, 13, 19, 3, 5, 127, 23, 89, 5, 17, 29, 37, 73, 7, 13, 31, 29, 113, 37, 109, 17, 257, 3, 31, 47, 31, 151, 43, 127, 7, 23, 41, 73, 109, 53, 157, 3, 11, 257, 7, 19, 67, 31, 331, 5, 29, 73, 5, 7, 17, 19, 3, 17, 251, 7, 13, 151, 59, 233, 11, 31, 41, 43, 337, 23, 683, 7, 31, 73, 5, 13

Offset: 1

Felix Fröhlich, Aug 16 2014

			The first three Poulet numbers (2-pseudoprimes) are 341 = 11*31, 561 = 3*11*17, and 645 = 3*5*43, so the sequence begins:
11, 31;
3, 11, 17;
3, 5, 43;
etc.

Felix Fröhlich, Table of n, a(n) for n = 1..2165 (all terms up to 10^7)

Cf. A001567, A007011, A084653, A084654, A084655.

forcomposite(n=1, 1e4, if(Mod(2, n)^(n-1)==1, f=factor(n)[, 1]; for(i=1, #f, print1(f[i], ", "))))

cp's OEIS Frontend

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

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