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A316468 Matula-Goebel numbers of locally stable rooted trees, meaning no branch is a submultiset of any other branch of the same root.

%I A316468 #6 Jul 05 2018 02:30:12
%S A316468 1,2,3,4,5,7,8,9,11,15,16,17,19,23,25,27,31,32,33,35,45,47,49,51,53,
%T A316468 55,59,64,67,69,75,77,81,83,85,93,95,97,99,103,119,121,125,127,128,
%U A316468 131,135,137,141,149,153,155,161,165,175,177,187,197,201,207,209
%N A316468 Matula-Goebel numbers of locally stable rooted trees, meaning no branch is a submultiset of any other branch of the same root.
%C A316468 A prime index of n is a number m such that prime(m) divides n. A number is in the sequence iff its distinct prime indices are pairwise indivisible and already belong to the sequence.
%e A316468 Sequence of locally stable rooted trees preceded by their Matula-Goebel numbers begins:
%e A316468    1: o
%e A316468    2: (o)
%e A316468    3: ((o))
%e A316468    4: (oo)
%e A316468    5: (((o)))
%e A316468    7: ((oo))
%e A316468    8: (ooo)
%e A316468    9: ((o)(o))
%e A316468   11: ((((o))))
%e A316468   15: ((o)((o)))
%e A316468   16: (oooo)
%e A316468   17: (((oo)))
%e A316468   19: ((ooo))
%e A316468   23: (((o)(o)))
%e A316468   25: (((o))((o)))
%e A316468   27: ((o)(o)(o))
%e A316468   31: (((((o)))))
%t A316468 primeMS[n_]:=If[n===1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A316468 Select[Range[100],Or[#==1,And[Select[Tuples[primeMS[#],2],UnsameQ@@#&&Divisible@@#&]=={},And@@#0/@primeMS[#]]]&]
%Y A316468 Cf. A000081, A004111, A007097, A112798, A277098, A285572, A285573, A303362, A304713, A316467, A316470, A316473, A316475, A316476, A316495.
%K A316468 nonn
%O A316468 1,2
%A A316468 _Gus Wiseman_, Jul 04 2018