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

Author

Gus Wiseman, Jan 19 2018

Keywords

• nonn

Examples

			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))))
		

Crossrefs

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

Programs

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]