A215150 Pseudoprimes divisible by a smaller pseudoprime.

13981, 18705, 23001, 55245, 63973, 72885, 75361, 107185, 126217, 129921, 137149, 157641, 158369, 172081, 176149, 188461, 215265, 266305, 272251, 276013, 278545, 285541, 294409, 348161, 387731, 423793, 464185, 488881, 493697, 617093, 625921, 743665, 748657, 825265

Offset

1,1

Comments

Here pseudoprime means a Fermat base-2 pseudoprime (a member of A001567).

Pseudoprimes by which the numbers from sequence are divisible: 341, 645, 561, 1905, 1729, 645, 341, 1105, 1387 and 1729, 341, 2047, 561, 5461, 2821, 1387, 1729, 1905, 1105, 2047, 1387, 2465 and 3277, 4681, 2701 and 4033 and 7957, 341, 5461, 4369, 5461, 2701, 4369, 5461, 10261, 1105, 1729, 1387 and 11305.

A pseudoprime can be divisible by more than one pseudoprime: e.g. 126217, 278545, 294409, 825265.

Links

Arkadiusz Wesolowski, Table of n, a(n) for n = 1..1000

G. L. Honaker, Jr. and Chris Caldwell, Prime Curios! 13981

Eric Weisstein's World of Mathematics, Poulet Number

Index entries for sequences related to pseudoprimes

Example

Since 2^13980 = 1 mod 13981 and 13981 = 11 * 31 * 41, 13981 is a pseudoprime, and it is divisible by 341, a smaller pseudoprime. 13981 is therefore in the sequence.
The pseudoprimes 75361, 129921, 348161, etc., are also divisible by 341.

Mathematica

lst1 = {}; lst2 = {}; r = 10^6; Do[If[! PrimeQ[n] && PowerMod[2, n - 1, n] == 1, AppendTo[lst1, n]], {n, 1, r, 2}]; l = Length[lst1]; Do[p = lst1[[a]]; b = 1; While[True, t = lst1[[b]]; If[p < 3*t, Break[]]; If[Divisible[p, t], AppendTo[lst2, p]; Break[]]; b++], {a, 2, l}]; lst2

Crossrefs

Cf. A001567, A214305.

Sequence in context: A031666 A031819 A066939 * A215944 A248999 A251612

Adjacent sequences: A215147 A215148 A215149 * A215151 A215152 A215153

Keyword

nonn

Author

Arkadiusz Wesolowski, Aug 04 2012

Status

approved