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A358577
Matula-Goebel numbers of "square" rooted trees, i.e., whose height equals their number of leaves.
25
1, 4, 12, 14, 18, 19, 21, 27, 40, 52, 60, 68, 70, 74, 78, 86, 89, 90, 91, 92, 95, 100, 102, 105, 107, 111, 117, 119, 122, 129, 130, 134, 135, 138, 146, 150, 151, 153, 161, 163, 169, 170, 175, 176, 181, 183, 185, 195, 201, 206, 207, 215, 219, 221, 225, 227, 230
OFFSET
1,2
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.
FORMULA
A358552(a(n)) = A109129(a(n)).
EXAMPLE
The terms together with their corresponding rooted trees begin:
1: o
4: (oo)
12: (oo(o))
14: (o(oo))
18: (o(o)(o))
19: ((ooo))
21: ((o)(oo))
27: ((o)(o)(o))
40: (ooo((o)))
52: (oo(o(o)))
60: (oo(o)((o)))
68: (oo((oo)))
70: (o((o))(oo))
74: (o(oo(o)))
78: (o(o)(o(o)))
86: (o(o(oo)))
89: ((ooo(o)))
90: (o(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&]
CROSSREFS
Internals instead of leaves: A358576, counted by A358587, ordered A358588.
Internals instead of height: A358578, counted by A185650, ordered A358579.
These trees are counted by A358589, ordered A358590.
A000081 counts rooted trees, ordered A000108.
A034781 counts trees by nodes and height.
A055277 counts trees by nodes and leaves, ordered A001263.
Sequence in context: A031330 A052339 A310562 * A123076 A310563 A260257
KEYWORD
nonn
AUTHOR
Gus Wiseman, Nov 25 2022
STATUS
approved