login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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 open-ending families. But this sequence lists all the starting values of an aliquot sequence that lead to open-ending. 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 (* Jean-François Alcover, Sep 10 2015 *)

CROSSREFS

Cf. A098007, A216072, A008892, A115350.

Sequence in context: A121743 A084802 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified May 25 03:14 EDT 2019. Contains 323539 sequences. (Running on oeis4.)