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A298540
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Matula-Goebel numbers of rooted trees such that every branch of the root has a different number of nodes.
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1
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1, 2, 3, 5, 6, 7, 10, 11, 13, 14, 15, 17, 19, 21, 22, 23, 26, 29, 30, 31, 33, 34, 37, 38, 39, 41, 42, 43, 46, 47, 51, 53, 55, 57, 58, 59, 61, 62, 65, 66, 67, 69, 71, 73, 74, 77, 78, 79, 82, 83, 85, 86, 87, 89, 91, 93, 94, 95, 97, 101, 102, 103, 106, 107, 109
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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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Sequence of trees begins:
1 o
2 (o)
3 ((o))
5 (((o)))
6 (o(o))
7 ((oo))
10 (o((o)))
11 ((((o))))
13 ((o(o)))
14 (o(oo))
15 ((o)((o)))
17 (((oo)))
19 ((ooo))
21 ((o)(oo))
22 (o(((o))))
23 (((o)(o)))
26 (o(o(o)))
29 ((o((o))))
30 (o(o)((o)))
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MATHEMATICA
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nn=500;
primeMS[n_]:=If[n===1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
MGweight[n_]:=If[n===1, 1, 1+Total[MGweight/@primeMS[n]]];
Select[Range[nn], UnsameQ@@MGweight/@primeMS[#]&]
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CROSSREFS
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Cf. A000081, A007097, A061775, A111299, A214577, A276625, A290760, A291442, A297571, A298479, A298534, A298536, A298538, A298539.
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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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