A298126 Matula-Goebel numbers of rooted trees in which all outdegrees are even.

1, 4, 14, 16, 49, 56, 64, 86, 106, 196, 224, 256, 301, 344, 371, 424, 454, 526, 622, 686, 784, 886, 896, 1024, 1154, 1204, 1376, 1484, 1589, 1696, 1816, 1841, 1849, 2104, 2177, 2279, 2386, 2401, 2488, 2744, 2809, 2846, 3101, 3136, 3238, 3544, 3584, 3986, 4039

Offset: 1

Author

Gus Wiseman, Jan 13 2018

Keywords

• nonn

Examples

			Sequence of trees begins:
1   o
4   (oo)
14  (o(oo))
16  (oooo)
49  ((oo)(oo))
56  (ooo(oo))
64  (oooooo)
86  (o(o(oo)))
106 (o(oooo))
196 (oo(oo)(oo))
224 (ooooo(oo))
256 (oooooooo)
301 ((oo)(o(oo)))
344 (ooo(o(oo)))
371 ((oo)(oooo))
424 (ooo(oooo))
454 (o((oo)(oo)))
526 (o(ooo(oo)))
622 (o(oooooo))
686 (o(oo)(oo)(oo))
784 (oooo(oo)(oo))
886 (o(o(o(oo))))
896 (ooooooo(oo))
		

Links

• Index entries for sequences related to Matula-Goebel numbers

Crossrefs

Cf. A000081, A001190, A007097, A026424, A028260, A061775, A111299, A214577, A245824, A276625, A277098, A290760, A291441, A291442, A291636, A295461, A297571, A298118, A298120.

Programs

Mathematica

primeMS[n_]:=If[n===1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
etQ[n_]:=Or[n===1,With[{m=primeMS[n]},EvenQ@Length@m&&And@@etQ/@m]];
Select[Range[10000],etQ]