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

%I A298126 #9 Oct 23 2021 21:17:16
%S A298126 1,4,14,16,49,56,64,86,106,196,224,256,301,344,371,424,454,526,622,
%T A298126 686,784,886,896,1024,1154,1204,1376,1484,1589,1696,1816,1841,1849,
%U A298126 2104,2177,2279,2386,2401,2488,2744,2809,2846,3101,3136,3238,3544,3584,3986,4039
%N A298126 Matula-Goebel numbers of rooted trees in which all outdegrees are even.
%H A298126 <a href="/index/Mat#matula">Index entries for sequences related to Matula-Goebel numbers</a>
%e A298126 Sequence of trees begins:
%e A298126 1   o
%e A298126 4   (oo)
%e A298126 14  (o(oo))
%e A298126 16  (oooo)
%e A298126 49  ((oo)(oo))
%e A298126 56  (ooo(oo))
%e A298126 64  (oooooo)
%e A298126 86  (o(o(oo)))
%e A298126 106 (o(oooo))
%e A298126 196 (oo(oo)(oo))
%e A298126 224 (ooooo(oo))
%e A298126 256 (oooooooo)
%e A298126 301 ((oo)(o(oo)))
%e A298126 344 (ooo(o(oo)))
%e A298126 371 ((oo)(oooo))
%e A298126 424 (ooo(oooo))
%e A298126 454 (o((oo)(oo)))
%e A298126 526 (o(ooo(oo)))
%e A298126 622 (o(oooooo))
%e A298126 686 (o(oo)(oo)(oo))
%e A298126 784 (oooo(oo)(oo))
%e A298126 886 (o(o(o(oo))))
%e A298126 896 (ooooooo(oo))
%t A298126 primeMS[n_]:=If[n===1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A298126 etQ[n_]:=Or[n===1,With[{m=primeMS[n]},EvenQ@Length@m&&And@@etQ/@m]];
%t A298126 Select[Range[10000],etQ]
%Y A298126 Cf. A000081, A001190, A007097, A026424, A028260, A061775, A111299, A214577, A245824, A276625, A277098, A290760, A291441, A291442, A291636, A295461, A297571, A298118, A298120.
%K A298126 nonn
%O A298126 1,2
%A A298126 _Gus Wiseman_, Jan 13 2018