OFFSET
1,1
COMMENTS
The Matula-Goebel number of a rooted tree is the product of primes indexed by the Matula-Goebel numbers of the branches of its root, which gives a bijective correspondence between positive integers and unlabeled rooted trees.
LINKS
EXAMPLE
The terms together with their corresponding rooted trees begin:
18: (o(o)(o))
21: ((o)(oo))
60: (oo(o)((o)))
70: (o((o))(oo))
78: (o(o)(o(o)))
91: ((oo)(o(o)))
92: (oo((o)(o)))
95: (((o))(ooo))
102: (o(o)((oo)))
111: ((o)(oo(o)))
119: ((oo)((oo)))
122: (o(o(o)(o)))
129: ((o)(o(oo)))
146: (o((o)(oo)))
151: ((oo(o)(o)))
181: ((o(o)(oo)))
201: ((o)((ooo)))
227: (((oo)(oo)))
MATHEMATICA
MGTree[n_]:=If[n==1, {}, MGTree/@Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
Select[Range[100], Count[MGTree[#], _[__], {0, Infinity}]==Count[MGTree[#], {}, {0, Infinity}]==Depth[MGTree[#]]-1&]
CROSSREFS
A034781 counts rooted trees by nodes and height.
KEYWORD
nonn
AUTHOR
Gus Wiseman, Nov 25 2022
STATUS
approved