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A131884
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Numbers conjectured to have an infinite, aperiodic, aliquot sequence.
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7
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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
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refs;
listen;
history;
text;
internal format)
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OFFSET
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1,1
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COMMENTS
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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
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LINKS
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MATHEMATICA
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(* 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 *)
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CROSSREFS
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KEYWORD
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hard,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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