A298534 Matula-Goebel numbers of rooted trees such that every branch of the root has the same number of leaves.

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, 43, 44, 45, 47, 48, 49, 50, 53, 54, 55, 59, 60, 61, 62, 64, 66, 67, 71, 72, 73, 75, 79, 80, 81, 83, 88, 89, 90, 91, 93, 96, 97, 99, 100

Offset

1,2

Links

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

Example

Sequence of trees begins:
1  o
2  (o)
3  ((o))
4  (oo)
5  (((o)))
6  (o(o))
7  ((oo))
8  (ooo)
9  ((o)(o))
10 (o((o)))
11 ((((o))))
12 (oo(o))
13 ((o(o)))
15 ((o)((o)))
16 (oooo)
17 (((oo)))
18 (o(o)(o))
19 ((ooo))
20 (oo((o)))
22 (o(((o))))
23 (((o)(o)))
24 (ooo(o))
25 (((o))((o)))
27 ((o)(o)(o))
29 ((o((o))))
30 (o(o)((o)))

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]]]];
Select[Range[nn], SameQ@@leafcount/@primeMS[#]&]

Crossrefs

Cf. A000081, A007097, A061775, A111299, A214577, A276625, A290760, A290822, A291442, A298533, A298536.

Sequence in context: A004440 A026495 A004437 * A291442 A236866 A122526

Adjacent sequences: A298531 A298532 A298533 * A298535 A298536 A298537

Keyword

nonn

Author

Gus Wiseman, Jan 20 2018

Status

approved