A298424 Matula-Goebel numbers of rooted trees in which all positive outdegrees are the same.

1, 2, 3, 4, 5, 8, 11, 14, 16, 31, 32, 49, 64, 76, 86, 127, 128, 256, 301, 424, 454, 512, 709, 722, 886, 1024, 1532, 1589, 1849, 2048, 2096, 3101, 3986, 4096, 5381, 6418, 6859, 8192, 9761, 9952, 11236, 13766, 13951, 14554, 16384, 19049, 21884, 22463, 23512

Offset

1,2

Links

Table of n, a(n) for n=1..49.

Example

Sequence of trees begins:
1   o
2   (o)
3   ((o))
4   (oo)
5   (((o)))
8   (ooo)
11  ((((o))))
14  (o(oo))
16  (oooo)
31  (((((o)))))
32  (ooooo)
49  ((oo)(oo))
64  (oooooo)
76  (oo(ooo))
86  (o(o(oo)))
127 ((((((o))))))
128 (ooooooo)
256 (oooooooo)
301 ((oo)(o(oo)))
424 (ooo(oooo))
454 (o((oo)(oo)))
512 (ooooooooo)
709 (((((((o)))))))
722 (o(ooo)(ooo))
886 (o(o(o(oo))))

Mathematica

MGtree[n_]:=If[n===1, {}, MGtree/@Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
soQ[n_]:=Or[n===1, SameQ@@Length/@Cases[MGtree[n], {__}, {0, Infinity}]];
Select[Range[1000], soQ]

Crossrefs

Cf. A000081, A000598, A001190, A003238, A007097, A111299, A214577, A276625, A298422, A298423, A298426.

Sequence in context: A281493 A181341 A174181 * A008812 A343608 A144679

Adjacent sequences: A298421 A298422 A298423 * A298425 A298426 A298427

Keyword

nonn

Author

Gus Wiseman, Jan 19 2018

Status

approved