A216072 -id:A216072 - cp's OEIS frontend

A284277 Primitive terms of A216072.

276, 564, 660, 966, 1074, 1134, 1464, 1476, 1488, 1512, 1560, 1578, 1632, 1734, 1920, 1992, 2232, 2340, 2360, 2514, 2664, 2712, 2982, 3270, 3366, 3408, 3432, 3564, 3678, 3774, 3876, 3906, 4116, 4224, 4290, 4350, 4380, 4788, 4800, 4842

Offset: 1

Sergey Pavlov, Mar 24 2017

In other words, such terms of A216072 that cannot be written as k*t where k is an integer, k > 1, t is a term of A216072.

			Since 276 is the first term of A216072, the number is in the sequence. But A216072(2) = 552 is not, because A216072(2) = 2 * A216072(1) = 2 * 276.

Cf. A216072.

A131884 Numbers conjectured to have an infinite, aperiodic, aliquot sequence.

Original entry on oeis.org

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

Offset: 1

J. Lowell, Oct 24 2007

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

Christophe Clavier: Aliquot sequences (with leading term < 10,000).
Wolfgang Creyaufmüller: Primzahlfamilien - aliquot sequences.
Paul Zimmermann: Aliquot sequences.

Cf. A098007, A216072, A008892, A115350.

(* 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 *)

More terms and links from Martin Renner, Oct 28 2011

cp's OEIS Frontend

A284277 Primitive terms of A216072.

Views

Author

Keywords

Comments

Examples

Crossrefs

A131884 Numbers conjectured to have an infinite, aperiodic, aliquot sequence.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

Extensions