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A324970 Matula-Goebel numbers of rooted identity trees where not all terminal subtrees are different.

%I A324970 #7 Mar 22 2019 00:33:41
%S A324970 15,30,33,39,47,55,65,66,78,87,93,94,110,113,123,130,137,141,143,145,
%T A324970 155,165,167,174,186,195,205,211,226,235,237,246,257,274,282,286,290,
%U A324970 303,310,313,317,319,327,330,334,339,341,377,381,390,395,397,403,410
%N A324970 Matula-Goebel numbers of rooted identity trees where not all terminal subtrees are different.
%C A324970 A rooted identity tree is an unlabeled rooted tree with no repeated branches directly under the same root.
%H A324970 Gus Wiseman, <a href="/A324970/a324970.png">The first 36 trees together with their Matula-Goebel numbers</a>.
%F A324970 Complement of A324935 in A276625.
%e A324970 The sequence of trees together with the Matula-Goebel numbers begins:
%e A324970    15: ((o)((o)))
%e A324970    30: (o(o)((o)))
%e A324970    33: ((o)(((o))))
%e A324970    39: ((o)(o(o)))
%e A324970    47: (((o)((o))))
%e A324970    55: (((o))(((o))))
%e A324970    65: (((o))(o(o)))
%e A324970    66: (o(o)(((o))))
%e A324970    78: (o(o)(o(o)))
%e A324970    87: ((o)(o((o))))
%e A324970    93: ((o)((((o)))))
%e A324970    94: (o((o)((o))))
%e A324970   110: (o((o))(((o))))
%e A324970   113: ((o(o)((o))))
%e A324970   123: ((o)((o(o))))
%e A324970   130: (o((o))(o(o)))
%e A324970   137: (((o)(((o)))))
%e A324970   141: ((o)((o)((o))))
%e A324970   143: ((((o)))(o(o)))
%e A324970   145: (((o))(o((o))))
%e A324970   155: (((o))((((o)))))
%e A324970   165: ((o)((o))(((o))))
%e A324970   167: (((o)(o(o))))
%e A324970   174: (o(o)(o((o))))
%e A324970   186: (o(o)((((o)))))
%e A324970   195: ((o)((o))(o(o)))
%t A324970 mgtree[n_Integer]:=If[n==1,{},mgtree/@Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A324970 Select[Range[100],And[And@@Cases[mgtree[#],q:{__}:>UnsameQ@@q,{0,Infinity}],!UnsameQ@@Cases[mgtree[#],{__},{0,Infinity}]]&]
%Y A324970 Cf. A000081, A004111, A007097, A196050, A276625, A317713, A324850, A324923, A324935, A324936, A324968, A324971, A324978.
%K A324970 nonn
%O A324970 1,1
%A A324970 _Gus Wiseman_, Mar 21 2019