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A358592
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Matula-Goebel numbers of rooted trees whose height, number of leaves, and number of internal (non-leaf) nodes are all equal.
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14
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18, 21, 60, 70, 78, 91, 92, 95, 102, 111, 119, 122, 129, 146, 151, 181, 201, 227, 264, 269, 308, 348, 376, 406, 418, 426, 452, 492, 497, 519, 551, 562, 574, 583, 596, 606, 659, 664, 668, 698, 707, 708, 717, 779, 794, 796, 809, 826, 834, 911, 932, 934, 942, 958
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OFFSET
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1,1
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COMMENTS
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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.
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LINKS
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FORMULA
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EXAMPLE
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The terms together with their corresponding rooted trees begin:
18: (o(o)(o))
21: ((o)(oo))
60: (oo(o)((o)))
70: (o((o))(oo))
78: (o(o)(o(o)))
91: ((oo)(o(o)))
92: (oo((o)(o)))
95: (((o))(ooo))
102: (o(o)((oo)))
111: ((o)(oo(o)))
119: ((oo)((oo)))
122: (o(o(o)(o)))
129: ((o)(o(oo)))
146: (o((o)(oo)))
151: ((oo(o)(o)))
181: ((o(o)(oo)))
201: ((o)((ooo)))
227: (((oo)(oo)))
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MATHEMATICA
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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}]==Depth[MGTree[#]]-1&]
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CROSSREFS
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A034781 counts rooted trees by nodes and height.
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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