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A347770 Conjectured list of numbers which are perfect, amicable, or sociable.

%I A347770 #32 Sep 18 2021 17:46:17
%S A347770 6,28,220,284,496,1184,1210,2620,2924,5020,5564,6232,6368,8128,10744,
%T A347770 10856,12285,12496,14264,14288,14316,14536,14595,15472,17296,17716,
%U A347770 18416,19116,19916,22744,22976,31704,45946,47616,48976,63020,66928,66992,67095,69615,71145,76084,79750
%N A347770 Conjectured list of numbers which are perfect, amicable, or sociable.
%C A347770 By definition, this is the union of A000396, A259180, and A122726. However, at present A122726 is not known to be complete. There is no proof that 564 (for example) is missing from this sequence. - _N. J. A. Sloane_, Sep 17 2021
%C A347770 Numbers m for which there exists k>=1 such that s^k(m) = m, where s is A001065.
%C A347770 Conjecture: There are no aliquot cycles containing even numbers and odd numbers simultaneously, i.e., every aliquot cycle either has only even numbers or has only odd numbers.
%H A347770 David Moews, <a href="http://djm.cc/amicable.txt">A list of amicable pairs below 2.01 * 10^11</a>
%H A347770 David Moews, <a href="http://djm.cc/amicable2.txt">A list of the first 5001 amicable pairs</a>
%H A347770 David Moews, <a href="http://djm.cc/sociable.txt">A list of currently known aliquot cycles of length greater than 2</a> [This list is not known to be complete.]
%H A347770 Jan Munch Pedersen, <a href="https://web.archive.org/web/20140502102524/http://amicable.homepage.dk/tables.htm">Tables of Aliquot Cycles</a> (from wayback machine)
%H A347770 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PerfectNumber.html">Perfect number</a>
%H A347770 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/AmicablePair.html">Amicable Pair</a>
%H A347770 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/SociableNumbers.html">Sociable Numbers</a>
%H A347770 Wikipedia, <a href="https://en.wikipedia.org/wiki/Perfect_number">Perfect number</a>
%H A347770 Wikipedia, <a href="https://en.wikipedia.org/wiki/Amicable_number">Amicable number</a>
%H A347770 Wikipedia, <a href="https://en.wikipedia.org/wiki/Sociable_number">Sociable number</a>
%e A347770 Known aliquot cycles (sorted by smallest member):
%e A347770 {6}
%e A347770 {28}
%e A347770 {220, 284}
%e A347770 {496}
%e A347770 {1184, 1210}
%e A347770 {2620, 2924}
%e A347770 {5020, 5564}
%e A347770 {6232, 6368}
%e A347770 {8128}
%e A347770 {10744, 10856}
%e A347770 {12285, 14595}
%e A347770 {12496, 14288, 15472, 14536, 14264}
%e A347770 {14316, 19116, 31704, 47616, 83328, 177792, 295488, 629072, 589786, 294896, 358336, 418904, 366556, 274924, 275444, 243760, 376736, 381028, 285778, 152990, 122410, 97946, 48976, 45946, 22976, 22744, 19916, 17716}
%e A347770 {17296, 18416}
%e A347770 ...
%Y A347770 Cf. A000396, A002025, A002046, A003416, A063990, A122726, A206708, A259180.
%K A347770 nonn
%O A347770 1,1
%A A347770 _Eric Chen_, Sep 13 2021
%E A347770 Edited with new definition (pointing out that the list is only conjectured to be complete) by _N. J. A. Sloane_, Sep 17 2021