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A280994 Triangle read by rows giving Matula-Goebel numbers of planted achiral trees with n nodes.

%I A280994 #7 Jan 12 2017 15:59:42
%S A280994 1,2,3,4,5,7,8,9,11,16,17,19,23,31,32,53,59,67,25,27,49,64,83,127,131,
%T A280994 241,277,331,97,103,128,227,311,431,709,739,1523,1787,2221,81,121,256,
%U A280994 289,361,509,563,719,1433,2063,3001,5381,5623,12763,15299,19577
%N A280994 Triangle read by rows giving Matula-Goebel numbers of planted achiral trees with n nodes.
%C A280994 An achiral tree is either (case 1) a single node or (case 2) a finite constant sequence (t,t,..,t) of achiral trees. Only in case 2 is an achiral tree considered to be a generalized Bethe tree (according to A214577).
%H A280994 E. Deutsch, <a href="http://arxiv.org/abs/1111.4288"> Rooted tree statistics from Matula numbers</a>, arXiv:1111.4288 [math.CO], 2011.
%e A280994 Triangle begins:
%e A280994 1,
%e A280994 2,
%e A280994 3, 4,
%e A280994 5, 7, 8,
%e A280994 9, 11, 16, 17, 19,
%e A280994 23, 31, 32, 53, 59, 67,
%e A280994 25, 27, 49, 64, 83, 127, 131, 241, 277, 331.
%t A280994 nn=7;MGNumber[_[]]:=1;MGNumber[x:_[__]]:=If[Length[x]===1,Prime[MGNumber[x[[1]]]],Times@@Prime/@MGNumber/@x];
%t A280994 cits[n_]:=If[n===1,{1},Join@@Table[ConstantArray[#,(n-1)/d]&/@cits[d],{d,Divisors[n-1]}]];
%t A280994 Table[Sort[MGNumber/@(cits[n]/.(1->{}))],{n,nn}]
%Y A280994 Cf. A003238 (row lengths), A214577, A061773, A061775, A004111, A007097, A196545, A275870.
%K A280994 nonn,tabf
%O A280994 1,2
%A A280994 _Gus Wiseman_, Jan 12 2017