A298305 - OEIS

%I #6 Jan 17 2018 04:28:40

%S 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,

%T 92,96,98,104,108,112,117,126,128,138,144,147,152,156,162,168,182,184,

%U 189,192,196,207,208,216,224,228,234,243,252,256,273,276,288,294

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

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

%e Sequence of trees begins:

%e 1  o

%e 2  (o)

%e 4  (oo)

%e 6  (o(o))

%e 8  (ooo)

%e 9  ((o)(o))

%e 12 (oo(o))

%e 16 (oooo)

%e 18 (o(o)(o))

%e 24 (ooo(o))

%e 27 ((o)(o)(o))

%e 28 (oo(oo))

%e 32 (ooooo)

%e 36 (oo(o)(o))

%e 42 (o(o)(oo))

%e 48 (oooo(o))

%e 52 (oo(o(o)))

%e 54 (o(o)(o)(o))

%e 56 (ooo(oo))

%e 63 ((o)(o)(oo))

%e 64 (oooooo)

%e 72 (ooo(o)(o))

%e 78 (o(o)(o(o)))

%e 81 ((o)(o)(o)(o))

%e 84 (oo(o)(oo))

%e 92 (oo((o)(o)))

%e 96 (ooooo(o))

%e 98 (o(oo)(oo))

%t MGtree[n_]:=If[n===1,{},MGtree/@Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];

%t strthinQ[t_]:=And@@Cases[t,b_List:>Length[b]>Max@@Length/@b,{0,Infinity}];

%t Select[Range[200],strthinQ[MGtree[#]]&]

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

%K nonn

%O 1,2

%A _Gus Wiseman_, Jan 16 2018