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.
Node-height is the number of nodes in the longest path from root to leaf.
LINKS
EXAMPLE
The terms together with their corresponding rooted trees begin:
9: ((o)(o))
15: ((o)((o)))
18: (o(o)(o))
21: ((o)(oo))
23: (((o)(o)))
30: (o(o)((o)))
33: ((o)(((o))))
35: (((o))(oo))
36: (oo(o)(o))
39: ((o)(o(o)))
42: (o(o)(oo))
46: (o((o)(o)))
47: (((o)((o))))
49: ((oo)(oo))
51: ((o)((oo)))
57: ((o)(ooo))
60: (oo(o)((o)))
61: ((o(o)(o)))
MATHEMATICA
MGTree[n_]:=If[n==1, {}, MGTree/@Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
Select[Range[100], Count[MGTree[#], _[__], {0, Infinity}]==Depth[MGTree[#]]-1&]
KEYWORD
nonn
AUTHOR
Gus Wiseman, Nov 25 2022
STATUS
approved