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%I #30 Mar 08 2014 12:13:25
%S 356408,399592,643336,652664,5232010,5799542,9363584,9437056,10596368,
%T 11199112,15363832,16517768,31818952,32205616,34352624,34860248,
%U 46237730,48641584,48852176,49215166,52695376,55349570,56208368,61319902,91996816,93259184
%N Untouchable amicable numbers: amicable pairs which cannot be reached by any aliquot sequence starting from a number that does not belong to this pair.
%C A pair of numbers x and y is called an untouchable amicable pair if x and y are amicable numbers (see A063990) and if x and y each have only one aliquot antecedent: the other number of their pair. In other words, they are amicable pairs which no aliquot sequence starting on a number that does not belong to this pair can reach.
%C The sequence lists the untouchable amicable numbers in increasing order. Note that the pairs x, y are not always adjacent to each other in the list.
%C Numbers that are the smaller number of their untouchable amicable pair are 356408, 643336, 5232010, 9363584, 10596368, 15363832, 31818952, 32205616, ... (subsequence of A002025).
%C The remaining numbers in the sequence are the larger number of their untouchable amicable pair: 399592, 652664, 5799542, 9437056, 11199112, 16517768, 34860248, 34352624, ... (subsequence of A002046).
%C We can call those pairs "untouchable amicable pairs", "isolated amicable pairs", or "isolated amicable cycles with two links" ... .
%H Jean-Luc Garambois, <a href="http://www.aliquotes.com">Aliquot sequences</a> (in French, but with an English summary).
%H Jean-Luc Garambois, <a href="http://www.aliquotes.com/ami.sage">Python program</a>
%Y Cf. A063990, A048138, A001065.
%K nonn
%O 1,1
%A _Jean Luc Garambois_, Mar 03 2014
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