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A358726
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Difference between the node-height and the number of leaves in the rooted tree with Matula-Goebel number n.
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6
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0, 1, 2, 0, 3, 1, 1, -1, 1, 2, 4, 0, 2, 0, 2, -2, 2, 0, 0, 1, 0, 3, 2, -1, 2, 1, 0, -1, 3, 1, 5, -3, 3, 1, 1, -1, 1, -1, 1, 0, 3, -1, 1, 2, 1, 1, 3, -2, -1, 1, 1, 0, -1, -1, 3, -2, -1, 2, 3, 0, 1, 4, -1, -4, 1, 2, 1, 0, 1, 0, 2, -2, 1, 0, 1, -2, 2, 0, 4, -1
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OFFSET
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1,3
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COMMENTS
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Node-height is the number of nodes 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.
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LINKS
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FORMULA
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EXAMPLE
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The tree (oo(oo(o))) with Matula-Goebel number 148 has node-height 4 and 5 leaves, so a(148) = -1.
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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}]]]];
Table[(Depth[MGTree[n]]-1)-Count[MGTree[n], {}, {0, Infinity}], {n, 1000}]
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CROSSREFS
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Positions of first appearances are A007097 and latter terms of A000079.
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KEYWORD
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sign
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AUTHOR
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STATUS
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approved
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