OFFSET
1,1
COMMENTS
These are paths with a single extra leaf growing from them.
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.
EXAMPLE
The terms together with their corresponding rooted trees begin:
4: (oo)
6: (o(o))
7: ((oo))
10: (o((o)))
13: ((o(o)))
17: (((oo)))
22: (o(((o))))
29: ((o((o))))
41: (((o(o))))
59: ((((oo))))
62: (o((((o)))))
79: ((o(((o)))))
109: (((o((o)))))
179: ((((o(o)))))
254: (o(((((o))))))
277: (((((oo)))))
293: ((o((((o))))))
401: (((o(((o))))))
599: ((((o((o))))))
MATHEMATICA
MGTree[n_]:=If[n==1, {}, MGTree/@Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
Select[Range[1000], Count[MGTree[#], _, {0, Infinity}]==Depth[MGTree[#]]&]
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Gus Wiseman, Dec 01 2022
STATUS
approved