OFFSET

1,1

COMMENTS

Edge-height (A109082) is the number of edges in the longest path from root to leaf.

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 trees begin:

9: ((o)(o))

15: ((o)((o)))

18: (o(o)(o))

21: ((o)(oo))

23: (((o)(o)))

25: (((o))((o)))

27: ((o)(o)(o))

30: (o(o)((o)))

33: ((o)(((o))))

35: (((o))(oo))

36: (oo(o)(o))

39: ((o)(o(o)))

42: (o(o)(oo))

45: ((o)(o)((o)))

46: (o((o)(o)))

47: (((o)((o))))

49: ((oo)(oo))

50: (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[#]]-2&]

CROSSREFS

KEYWORD

nonn

AUTHOR

Gus Wiseman, Nov 29 2022

STATUS

approved