

A131884


Numbers conjectured to have an infinite, aperiodic, aliquot sequence.


6



276, 306, 396, 552, 564, 660, 696, 780, 828, 888, 966, 996, 1074, 1086, 1098, 1104, 1134, 1218, 1302, 1314, 1320, 1338, 1350, 1356, 1392, 1398, 1410, 1464, 1476, 1488, 1512, 1560, 1572, 1578, 1590, 1632, 1650, 1662, 1674, 1722, 1734, 1758, 1770, 1806, 1836
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,1


COMMENTS

From Martin Renner, Oct 28 2011: (Start)
There are 12 numbers up to 1000 with the five yet unknown trajectories
(1) 276 >
306 > 396 > 696 > ...
(2) 552 > 888 > ...
(3) 564 > 780 > ...
(4) 660 >
828 >
996 > 1356 > ...
(5) 966 > 1338 > ...
The least starting numbers 276, 552, 564, 660 and 966 for the trajectories are called Lehmer five.
There are currently 81 open end trajectories up to 10000. (End)
Sequence A216072 lists only the values that are the lowest starting elements of open end aliquot sequences that are the part of different openending families. But this sequence lists all the starting values of an aliquot sequence that lead to openending. It includes all values obtained by iterating from the starting values of this sequence.  V. Raman, Dec 08 2012


LINKS

Table of n, a(n) for n=1..45.
Christophe Clavier: Aliquot sequences (with leading term < 10,000).
Wolfgang Creyaufmüller: Primzahlfamilien  aliquot sequences.
Paul Zimmermann: Aliquot sequences.


MATHEMATICA

(* This script is not suitable for a large number of terms *) maxAliquot = 10^50; A131884 = {}; s[1] = 1; s[n_] := DivisorSigma[1, n]  n; selQ[n_ /; n <= 5] = True; selQ[n_] := NestWhile[s, n, If[{##}[[1]] > maxAliquot, Print[n]; AppendTo[A131884, n]; False, Length[{##}] < 4  {##}[[4 ;; 3]] != {##}[[2 ;; 1]]] &, All] == 1; selQ /@ Range[1000]; A131884 (* JeanFrançois Alcover, Sep 10 2015 *)


CROSSREFS

Cf. A098007, A216072, A008892, A115350.
Sequence in context: A084802 A309998 A003903 * A284279 A228517 A008892
Adjacent sequences: A131881 A131882 A131883 * A131885 A131886 A131887


KEYWORD

hard,nonn


AUTHOR

J. Lowell, Oct 24 2007


EXTENSIONS

More terms and links from Martin Renner, Oct 28 2011


STATUS

approved



