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:
2: (o)
6: (o(o))
7: ((oo))
18: (o(o)(o))
20: (oo((o)))
21: ((o)(oo))
26: (o(o(o)))
34: (o((oo)))
37: ((oo(o)))
43: ((o(oo)))
54: (o(o)(o)(o))
60: (oo(o)((o)))
63: ((o)(o)(oo))
67: (((ooo)))
70: (o((o))(oo))
78: (o(o)(o(o)))
88: (ooo(((o))))
91: ((oo)(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}]==Count[MGTree[#], _[__], {0, Infinity}]&]
KEYWORD
nonn
AUTHOR
Gus Wiseman, Nov 25 2022
STATUS
approved