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A298363 Matula-Goebel numbers of rooted identity trees with thinning limbs.

%I A298363 #5 Jan 19 2018 02:07:26
%S A298363 1,2,3,5,6,10,11,15,22,26,30,31,33,39,55,58,62,65,66,78,87,93,94,110,
%T A298363 127,130,141,143,145,155,158,165,174,186,195,202,235,237,254,274,282,
%U A298363 286,290,303,310,319,330,334,341,377,381,390,395,403,411,429,435,465
%N A298363 Matula-Goebel numbers of rooted identity trees with thinning limbs.
%C A298363 An unlabeled rooted tree has thinning limbs if its outdegrees are weakly decreasing from root to leaves.
%F A298363 Intersection of A276625 and A298303.
%e A298363 Sequence of trees begins:
%e A298363 1  o
%e A298363 2  (o)
%e A298363 3  ((o))
%e A298363 5  (((o)))
%e A298363 6  (o(o))
%e A298363 10 (o((o)))
%e A298363 11 ((((o))))
%e A298363 15 ((o)((o)))
%e A298363 22 (o(((o))))
%e A298363 26 (o(o(o)))
%e A298363 30 (o(o)((o)))
%e A298363 31 (((((o)))))
%e A298363 33 ((o)(((o))))
%e A298363 39 ((o)(o(o)))
%e A298363 55 (((o))(((o))))
%e A298363 58 (o(o((o))))
%e A298363 62 (o((((o)))))
%e A298363 65 (((o))(o(o)))
%e A298363 66 (o(o)(((o))))
%e A298363 78 (o(o)(o(o)))
%e A298363 87 ((o)(o((o))))
%e A298363 93 ((o)((((o)))))
%e A298363 94 (o((o)((o))))
%t A298363 MGtree[n_]:=If[n===1,{},MGtree/@Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A298363 idthinQ[t_]:=And@@Cases[t,b_List:>UnsameQ@@b&&Length[b]>=Max@@Length/@b,{0,Infinity}];
%t A298363 Select[Range[500],idthinQ[MGtree[#]]&]
%Y A298363 Cf. A000081, A004111, A007097, A061775, A111299, A124343, A124346, A214577, A276625, A277098, A290689, A290760, A298304, A298305.
%K A298363 nonn
%O A298363 1,2
%A A298363 _Gus Wiseman_, Jan 17 2018