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A324842
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Matula-Goebel numbers of rooted trees where the branches of any branch of any terminal subtree form a submultiset of the branches of the same subtree.
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2
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1, 2, 4, 6, 8, 12, 16, 18, 24, 28, 32, 36, 48, 54, 56, 64, 72, 78, 84, 96, 108, 112, 128, 144, 152, 156, 162, 168, 192, 196, 216, 224, 234, 252, 256, 288, 304, 312, 324, 336, 384, 392, 432, 444, 448, 456, 468, 486, 504, 512, 576, 588, 608, 624, 648, 672, 702
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OFFSET
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1,2
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LINKS
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EXAMPLE
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The sequence of rooted trees together with their Matula-Goebel numbers begins:
1: o
2: (o)
4: (oo)
6: (o(o))
8: (ooo)
12: (oo(o))
16: (oooo)
18: (o(o)(o))
24: (ooo(o))
28: (oo(oo))
32: (ooooo)
36: (oo(o)(o))
48: (oooo(o))
54: (o(o)(o)(o))
56: (ooo(oo))
64: (oooooo)
72: (ooo(o)(o))
78: (o(o)(o(o)))
84: (oo(o)(oo))
96: (ooooo(o))
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MATHEMATICA
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primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
qaQ[n_]:=And[And@@Table[Divisible[n, x], {x, primeMS[n]}], And@@qaQ/@primeMS[n]];
Select[Range[1000], qaQ]
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CROSSREFS
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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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