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

1,2

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.

Links

Table of n, a(n) for n=1..67.

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]

Crossrefs

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

Sequence in context: A026495 A004437 A298534 * A236866 A122526 A120401

Adjacent sequences: A291439 A291440 A291441 * A291443 A291444 A291445

Keyword

nonn

Author

Gus Wiseman, Aug 23 2017

Status

approved