OFFSET
1,2
COMMENTS
An unlabeled rooted tree has strictly thinning limbs if its outdegrees are strictly decreasing from root to leaves.
EXAMPLE
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))
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[#]]&]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jan 16 2018
STATUS
approved