A298424 - OEIS

%I #6 Jan 19 2018 02:21:22

%S 1,2,3,4,5,8,11,14,16,31,32,49,64,76,86,127,128,256,301,424,454,512,

%T 709,722,886,1024,1532,1589,1849,2048,2096,3101,3986,4096,5381,6418,

%U 6859,8192,9761,9952,11236,13766,13951,14554,16384,19049,21884,22463,23512

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

%e Sequence of trees begins:

%e 1   o

%e 2   (o)

%e 3   ((o))

%e 4   (oo)

%e 5   (((o)))

%e 8   (ooo)

%e 11  ((((o))))

%e 14  (o(oo))

%e 16  (oooo)

%e 31  (((((o)))))

%e 32  (ooooo)

%e 49  ((oo)(oo))

%e 64  (oooooo)

%e 76  (oo(ooo))

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

%e 127 ((((((o))))))

%e 128 (ooooooo)

%e 256 (oooooooo)

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

%e 424 (ooo(oooo))

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

%e 512 (ooooooooo)

%e 709 (((((((o)))))))

%e 722 (o(ooo)(ooo))

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

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

%t soQ[n_]:=Or[n===1,SameQ@@Length/@Cases[MGtree[n],{__},{0,Infinity}]];

%t Select[Range[1000],soQ]

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

%K nonn

%O 1,2

%A _Gus Wiseman_, Jan 19 2018