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A298534
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Matula-Goebel numbers of rooted trees such that every branch of the root has the same number of leaves.
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4
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1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 15, 16, 17, 18, 19, 20, 22, 23, 24, 25, 27, 29, 30, 31, 32, 33, 36, 37, 40, 41, 43, 44, 45, 47, 48, 49, 50, 53, 54, 55, 59, 60, 61, 62, 64, 66, 67, 71, 72, 73, 75, 79, 80, 81, 83, 88, 89, 90, 91, 93, 96, 97, 99, 100
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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)))
6 (o(o))
7 ((oo))
8 (ooo)
9 ((o)(o))
10 (o((o)))
11 ((((o))))
12 (oo(o))
13 ((o(o)))
15 ((o)((o)))
16 (oooo)
17 (((oo)))
18 (o(o)(o))
19 ((ooo))
20 (oo((o)))
22 (o(((o))))
23 (((o)(o)))
24 (ooo(o))
25 (((o))((o)))
27 ((o)(o)(o))
29 ((o((o))))
30 (o(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], SameQ@@leafcount/@primeMS[#]&]
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CROSSREFS
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Cf. A000081, A007097, A061775, A111299, A214577, A276625, A290760, A290822, A291442, A298533, A298536.
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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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