reviewed

approved

proposed

reviewed

editing

proposed

Cf. A000081, A007097, A061775, A111299, A214577, A276625, A290689, A290760, A291442, A298534, A298535.

allocated for Gus WisemanMatula-Goebel numbers of rooted trees such that every branch of the root has a different number of leaves.

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

1,2

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))))

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[#]&]

Cf. A000081, A007097, A061775, A111299, A214577, A276625, A290760, A291442, A298534, A298535.

allocated

nonn

Gus Wiseman, Jan 20 2018

approved

editing

allocated for Gus Wiseman

allocated

approved