A298126 - OEIS

%I #9 Oct 23 2021 21:17:16

%S 1,4,14,16,49,56,64,86,106,196,224,256,301,344,371,424,454,526,622,

%T 686,784,886,896,1024,1154,1204,1376,1484,1589,1696,1816,1841,1849,

%U 2104,2177,2279,2386,2401,2488,2744,2809,2846,3101,3136,3238,3544,3584,3986,4039

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

%H <a href="/index/Mat#matula">Index entries for sequences related to Matula-Goebel numbers</a>

%e Sequence of trees begins:

%e 1   o

%e 4   (oo)

%e 14  (o(oo))

%e 16  (oooo)

%e 49  ((oo)(oo))

%e 56  (ooo(oo))

%e 64  (oooooo)

%e 86  (o(o(oo)))

%e 106 (o(oooo))

%e 196 (oo(oo)(oo))

%e 224 (ooooo(oo))

%e 256 (oooooooo)

%e 301 ((oo)(o(oo)))

%e 344 (ooo(o(oo)))

%e 371 ((oo)(oooo))

%e 424 (ooo(oooo))

%e 454 (o((oo)(oo)))

%e 526 (o(ooo(oo)))

%e 622 (o(oooooo))

%e 686 (o(oo)(oo)(oo))

%e 784 (oooo(oo)(oo))

%e 886 (o(o(o(oo))))

%e 896 (ooooooo(oo))

%t primeMS[n_]:=If[n===1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];

%t etQ[n_]:=Or[n===1,With[{m=primeMS[n]},EvenQ@Length@m&&And@@etQ/@m]];

%t Select[Range[10000],etQ]

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

%K nonn

%O 1,2

%A _Gus Wiseman_, Jan 13 2018