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A317789 Matula-Goebel numbers of rooted trees that are not locally nonintersecting.

%I A317789 #5 Aug 08 2018 07:53:41
%S A317789 9,21,23,25,27,39,46,49,57,63,65,69,73,81,83,87,91,92,97,103,111,115,
%T A317789 117,121,125,129,133,138,146,147,159,161,166,167,169,171,183,184,185,
%U A317789 189,194,199,203,206,207,213,219,227,230,235,237,243,247,249,253,259
%N A317789 Matula-Goebel numbers of rooted trees that are not locally nonintersecting.
%C A317789 An unlabeled rooted tree is locally nonintersecting if there is no common subbranch to all branches directly under any given node.
%e A317789 The sequence of rooted trees that are not locally nonintersecting together with their Matula-Goebel numbers begins:
%e A317789    9: ((o)(o))
%e A317789   21: ((o)(oo))
%e A317789   23: (((o)(o)))
%e A317789   25: (((o))((o)))
%e A317789   27: ((o)(o)(o))
%e A317789   39: ((o)(o(o)))
%e A317789   46: (o((o)(o)))
%e A317789   49: ((oo)(oo))
%e A317789   57: ((o)(ooo))
%e A317789   63: ((o)(o)(oo))
%e A317789   65: (((o))(o(o)))
%e A317789   69: ((o)((o)(o)))
%e A317789   73: (((o)(oo)))
%e A317789   81: ((o)(o)(o)(o))
%e A317789   83: ((((o)(o))))
%e A317789   87: ((o)(o((o))))
%e A317789   91: ((oo)(o(o)))
%e A317789   92: (oo((o)(o)))
%e A317789   97: ((((o))((o))))
%t A317789 rupQ[n_]:=Or[n==1,If[PrimeQ[n],rupQ[PrimePi[n]],And[GCD@@PrimePi/@FactorInteger[n][[All,1]]==1,And@@rupQ/@PrimePi/@FactorInteger[n][[All,1]]]]];
%t A317789 Select[Range[100],!rupQ[#]&]
%Y A317789 Cf. A000081, A184155, A276625, A316470, A316495, A316502, A317785, A317786, A317787.
%K A317789 nonn
%O A317789 1,1
%A A317789 _Gus Wiseman_, Aug 07 2018