This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A291442 #6 Sep 01 2017 05:02:33
%S A291442 1,2,3,4,5,6,7,8,9,10,11,12,13,15,16,17,18,19,20,22,23,24,25,27,29,30,
%T A291442 31,32,33,36,37,40,41,44,45,47,48,49,50,53,54,55,59,60,61,62,64,66,67,
%U A291442 71,72,75,79,80,81,83,88,89,90,91,93,96,97,99,100,103,108
%N A291442 Matula-Goebel numbers of leaf-balanced trees.
%C A291442 An unlabeled rooted tree is leaf-balanced if every branch has the same number of leaves and every non-leaf rooted subtree is also leaf-balanced.
%t A291442 nn=2000;
%t A291442 primeMS[n_]:=If[n===1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A291442 leafcount[n_]:=If[n===1,1,With[{m=primeMS[n]},If[Length[m]===1,leafcount[First[m]],Total[leafcount/@m]]]];
%t A291442 balQ[n_]:=Or[n===1,With[{m=primeMS[n]},And[SameQ@@leafcount/@m,And@@balQ/@m]]];
%t A291442 Select[Range[nn],balQ]
%Y A291442 Cf. A000081, A007097, A061775, A109129, A214577, A280994, A291441, A291443.
%K A291442 nonn
%O A291442 1,2
%A A291442 _Gus Wiseman_, Aug 23 2017