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A298538
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Matula-Goebel numbers of rooted trees such that every branch of the root has the same number of nodes.
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3
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1, 2, 3, 4, 5, 7, 8, 9, 11, 13, 16, 17, 19, 23, 25, 27, 29, 31, 32, 35, 37, 41, 43, 47, 49, 53, 59, 61, 64, 67, 71, 73, 79, 81, 83, 89, 97, 101, 103, 107, 109, 113, 121, 125, 127, 128, 131, 137, 139, 143, 149, 151, 157, 163, 167, 169, 173, 175, 179, 181, 187
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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))
4 (oo)
5 (((o)))
7 ((oo))
8 (ooo)
9 ((o)(o))
11 ((((o))))
13 ((o(o)))
16 (oooo)
17 (((oo)))
19 ((ooo))
23 (((o)(o)))
25 (((o))((o)))
27 ((o)(o)(o))
29 ((o((o))))
31 (((((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], SameQ@@MGweight/@primeMS[#]&]
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CROSSREFS
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Cf. A000081, A007097, A061775, A111299, A214577, A276625, A290760, A291442, A297571, A298478, A298534, A298536, A298537.
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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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