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%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
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