OFFSET
1,2
COMMENTS
A rooted identity tree is an unlabeled rooted tree with no repeated branches directly under the same root. This sequence ranks rooted identity trees satisfying the additional condition that all non-leaf terminal subtrees are different.
LINKS
EXAMPLE
The sequence of trees together with the Matula-Goebel numbers begins:
1: o
2: (o)
3: ((o))
5: (((o)))
6: (o(o))
10: (o((o)))
11: ((((o))))
13: ((o(o)))
22: (o(((o))))
26: (o(o(o)))
29: ((o((o))))
31: (((((o)))))
41: (((o(o))))
58: (o(o((o))))
62: (o((((o)))))
79: ((o(((o)))))
82: (o((o(o))))
101: ((o(o(o))))
109: (((o((o)))))
127: ((((((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