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%I #15 Jul 21 2023 15:29:21
%S 2,28,52,88,96,120,124,146,162,188,206,208,210,216,238,246,248,250,
%T 262,268,276,288,290,292,298,304,306,322,324,326,336,342,362,372,388,
%U 396,406,408,412,426,428,430,438,448,452,472,474,478,486,494,498,508,516
%N Numbers k such that there is no odd number whose aliquot sequence contains k.
%C k is in sequence iff k can never be reached when iterating the map x -> A001065(x) starting with any odd number m.
%C Assuming the stronger version of Goldbach conjecture, iff k is in the sequence, there are infinitely many odd numbers whose aliquot sequence contain k.
%C Supersequence of A005114 (except 5), A283152, A284147, A284156, A284187, ..., and untouchable perfect numbers (28, 137438691328, ...), untouchable amicable numbers (A238382), untouchable sociable numbers.
%H Andrew R. Booker, <a href="https://arxiv.org/abs/1610.07471">Finite connected components of the aliquot graph</a>, arXiv:1610.07471 [math.NT], 2017.
%H Jean-Luc Garambois, <a href="http://www.aliquotes.com/graphinfinisuali.htm">Le graphe infini des suites aliquotes</a> (in French).
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Aliquot_sequence">Aliquot sequence</a>
%Y Cf. A001065, A005114, A238382, A283152, A284147, A284156, A284187.
%K nonn
%O 1,1
%A _Jinyuan Wang_, Jun 25 2023