A298305 Matula-Goebel numbers of rooted trees with strictly thinning limbs.

1, 2, 4, 6, 8, 9, 12, 16, 18, 24, 27, 28, 32, 36, 42, 48, 52, 54, 56, 63, 64, 72, 78, 81, 84, 92, 96, 98, 104, 108, 112, 117, 126, 128, 138, 144, 147, 152, 156, 162, 168, 182, 184, 189, 192, 196, 207, 208, 216, 224, 228, 234, 243, 252, 256, 273, 276, 288, 294

Offset: 1

Author

Gus Wiseman, Jan 16 2018

Keywords

• nonn

Comments

An unlabeled rooted tree has strictly thinning limbs if its outdegrees are strictly decreasing from root to leaves.

Examples

			Sequence of trees begins:
1  o
2  (o)
4  (oo)
6  (o(o))
8  (ooo)
9  ((o)(o))
12 (oo(o))
16 (oooo)
18 (o(o)(o))
24 (ooo(o))
27 ((o)(o)(o))
28 (oo(oo))
32 (ooooo)
36 (oo(o)(o))
42 (o(o)(oo))
48 (oooo(o))
52 (oo(o(o)))
54 (o(o)(o)(o))
56 (ooo(oo))
63 ((o)(o)(oo))
64 (oooooo)
72 (ooo(o)(o))
78 (o(o)(o(o)))
81 ((o)(o)(o)(o))
84 (oo(o)(oo))
92 (oo((o)(o)))
96 (ooooo(o))
98 (o(oo)(oo))
		

Crossrefs

Cf. A000081, A007097, A061775, A111299, A124343, A124346, A214577, A276625, A290760, A291636, A298126, A298120, A298304.

Programs

Mathematica

MGtree[n_]:=If[n===1,{},MGtree/@Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
strthinQ[t_]:=And@@Cases[t,b_List:>Length[b]>Max@@Length/@b,{0,Infinity}];
Select[Range[200],strthinQ[MGtree[#]]&]