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A298536
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Matula-Goebel numbers of rooted trees such that every branch of the root has a different number of leaves.
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5
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1, 2, 3, 5, 7, 11, 13, 14, 17, 19, 21, 23, 26, 29, 31, 34, 35, 37, 38, 39, 41, 43, 46, 47, 51, 53, 57, 58, 59, 61, 65, 67, 69, 71, 73, 74, 77, 79, 82, 83, 85, 86, 87, 89, 94, 95, 97, 101, 103, 106, 107, 109, 111, 113, 115, 118, 122, 123, 127, 129, 131, 133
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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)))
7 ((oo))
11 ((((o))))
13 ((o(o)))
14 (o(oo))
17 (((oo)))
19 ((ooo))
21 ((o)(oo))
23 (((o)(o)))
26 (o(o(o)))
29 ((o((o))))
31 (((((o)))))
34 (o((oo)))
35 (((o))(oo))
37 ((oo(o)))
38 (o(ooo))
39 ((o)(o(o)))
41 (((o(o))))
43 ((o(oo)))
46 (o((o)(o)))
47 (((o)((o))))
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MATHEMATICA
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nn=2000;
primeMS[n_]:=If[n===1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
leafcount[n_]:=If[n===1, 1, With[{m=primeMS[n]}, If[Length[m]===1, leafcount[First[m]], Total[leafcount/@m]]]];
Select[Range[nn], UnsameQ@@leafcount/@primeMS[#]&]
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CROSSREFS
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Cf. A000081, A007097, A061775, A111299, A214577, A276625, A290689, A290760, A291442, A298534, A298535.
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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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