A291442 Matula-Goebel numbers of leaf-balanced trees.

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, 31, 32, 33, 36, 37, 40, 41, 44, 45, 47, 48, 49, 50, 53, 54, 55, 59, 60, 61, 62, 64, 66, 67, 71, 72, 75, 79, 80, 81, 83, 88, 89, 90, 91, 93, 96, 97, 99, 100, 103, 108

Offset: 1

Author

Gus Wiseman, Aug 23 2017

Keywords

• nonn

Comments

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.

Crossrefs

Cf. A000081, A007097, A061775, A109129, A214577, A280994, A291441, A291443.

Programs

Mathematica

nn=2000;
primeMS[n_]:=If[n===1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
leafcount[n_]:=If[n===1,1,With[{m=primeMS[n]},If[Length[m]===1,leafcount[First[m]],Total[leafcount/@m]]]];
balQ[n_]:=Or[n===1,With[{m=primeMS[n]},And[SameQ@@leafcount/@m,And@@balQ/@m]]];
Select[Range[nn],balQ]