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A324845 Matula-Goebel numbers of rooted trees where the branches of no non-leaf branch of any terminal subtree form a submultiset of the branches of the same subtree.

%I A324845 #6 Mar 19 2019 07:15:27
%S A324845 1,2,3,4,5,7,8,9,10,11,14,16,17,19,20,21,22,23,25,27,29,31,32,33,34,
%T A324845 35,38,40,43,44,46,49,50,51,53,57,58,59,62,63,64,67,68,69,70,71,73,76,
%U A324845 77,79,80,81,83,85,86,87,88,92,93,95,97,98,99,100,103,106
%N A324845 Matula-Goebel numbers of rooted trees where the branches of no non-leaf branch of any terminal subtree form a submultiset of the branches of the same subtree.
%H A324845 Gus Wiseman, <a href="/A324845/a324845.png">The sequence of rooted trees whose Matula-Goebel numbers belong to A324845</a>.
%e A324845 The sequence of terms together with their Matula-Goebel numbers begins:
%e A324845    1: o
%e A324845    2: (o)
%e A324845    3: ((o))
%e A324845    4: (oo)
%e A324845    5: (((o)))
%e A324845    7: ((oo))
%e A324845    8: (ooo)
%e A324845    9: ((o)(o))
%e A324845   10: (o((o)))
%e A324845   11: ((((o))))
%e A324845   14: (o(oo))
%e A324845   16: (oooo)
%e A324845   17: (((oo)))
%e A324845   19: ((ooo))
%e A324845   20: (oo((o)))
%e A324845   21: ((o)(oo))
%e A324845   22: (o(((o))))
%e A324845   23: (((o)(o)))
%e A324845   25: (((o))((o)))
%e A324845   27: ((o)(o)(o))
%t A324845 primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A324845 qaQ[n_]:=And[And@@Table[!Divisible[n,x],{x,DeleteCases[primeMS[n],1]}],And@@qaQ/@primeMS[n]];
%t A324845 Select[Range[100],qaQ]
%Y A324845 Cf. A000081, A007097, A290822, A306844, A318186.
%Y A324845 Cf. A324694, A324738, A324744, A324749, A324754, A324759, A324765, A324768, A324838, A324842, A324844, A324846, A324847, A324849.
%K A324845 nonn
%O A324845 1,2
%A A324845 _Gus Wiseman_, Mar 18 2019