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A318048 Size of the span of the unlabeled rooted tree with Matula-Goebel number n.

%I A318048 #8 Oct 23 2021 21:16:36
%S A318048 1,2,3,2,4,4,4,2,6,6,5,4,6,3,9,2,6,6,4,6,6,8,10,4,12,6,10,4,9,9,6,2,
%T A318048 12,6,9,6,6,4,9,6,9,7,6,8,15,10,15,4,5,12,9,7,4,10,16,4,7,9,8,9,10,10,
%U A318048 11,2,13,12,6,7,14,10,9,6,10,7,21,3,12,10,12,6
%N A318048 Size of the span of the unlabeled rooted tree with Matula-Goebel number n.
%C A318048 The span of a tree is defined to be the set of possible terminal subtrees of initial subtrees, or, which is the same, the set of possible initial subtrees of terminal subtrees.
%H A318048 <a href="/index/Mat#matula">Index entries for sequences related to Matula-Goebel numbers</a>
%e A318048 42 is the Matula-Goebel number of (o(o)(oo)), which has span {o, (o), (oo), (ooo), (oo(oo)), (o(o)o), (o(o)(oo))}, so a(42) = 7.
%t A318048 ext[c_,{}]:=c;ext[c_,s:{__}]:=Extract[c,s];rpp[c_,v_,{}]:=v;rpp[c_,v_,s:{__}]:=ReplacePart[c,v,s];
%t A318048 RLO[ear_,rue:{__}]:=Union@@(Function[x,rpp[ear,x,#2]]/@ReplaceList[ext[ear,#2],#1]&@@@Select[Tuples[{rue,Position[ear,_]}],MatchQ[ext[ear,#[[2]]],#[[1,1]]]&]);
%t A318048 RL[ear_,rue:{__}]:=FixedPoint[Function[keeps,Union[keeps,Join@@(RLO[#,rue]&/@keeps)]],{ear}];
%t A318048 primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A318048 MGTree[n_]:=If[n==1,{},MGTree/@primeMS[n]];
%t A318048 Table[Length[Union[Cases[RL[MGTree[n],{List[__List]:>List[]}],_List,{1,Infinity}]]],{n,100}]
%Y A318048 Cf. A000081, A007097, A007853, A049076, A061773, A061775, A109082, A109129, A206491, A317713, A318046.
%K A318048 nonn
%O A318048 1,2
%A A318048 _Gus Wiseman_, Aug 13 2018