OFFSET
1,1
COMMENTS
A rooted identity tree is an unlabeled rooted tree with no repeated branches directly under the same root.
LINKS
EXAMPLE
The sequence of trees together with the Matula-Goebel numbers begins:
15: ((o)((o)))
30: (o(o)((o)))
33: ((o)(((o))))
39: ((o)(o(o)))
47: (((o)((o))))
55: (((o))(((o))))
65: (((o))(o(o)))
66: (o(o)(((o))))
78: (o(o)(o(o)))
87: ((o)(o((o))))
93: ((o)((((o)))))
94: (o((o)((o))))
110: (o((o))(((o))))
113: ((o(o)((o))))
123: ((o)((o(o))))
130: (o((o))(o(o)))
137: (((o)(((o)))))
141: ((o)((o)((o))))
143: ((((o)))(o(o)))
145: (((o))(o((o))))
155: (((o))((((o)))))
165: ((o)((o))(((o))))
167: (((o)(o(o))))
174: (o(o)(o((o))))
186: (o(o)((((o)))))
195: ((o)((o))(o(o)))
MATHEMATICA
mgtree[n_Integer]:=If[n==1, {}, mgtree/@Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
Select[Range[100], And[And@@Cases[mgtree[#], q:{__}:>UnsameQ@@q, {0, Infinity}], !UnsameQ@@Cases[mgtree[#], {__}, {0, Infinity}]]&]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Mar 21 2019
STATUS
approved