cp's OEIS Frontend

A298424 Matula-Goebel numbers of rooted trees in which all positive outdegrees are the same.

%I A298424 #6 Jan 19 2018 02:21:22
%S A298424 1,2,3,4,5,8,11,14,16,31,32,49,64,76,86,127,128,256,301,424,454,512,
%T A298424 709,722,886,1024,1532,1589,1849,2048,2096,3101,3986,4096,5381,6418,
%U A298424 6859,8192,9761,9952,11236,13766,13951,14554,16384,19049,21884,22463,23512
%N A298424 Matula-Goebel numbers of rooted trees in which all positive outdegrees are the same.
%e A298424 Sequence of trees begins:
%e A298424 1   o
%e A298424 2   (o)
%e A298424 3   ((o))
%e A298424 4   (oo)
%e A298424 5   (((o)))
%e A298424 8   (ooo)
%e A298424 11  ((((o))))
%e A298424 14  (o(oo))
%e A298424 16  (oooo)
%e A298424 31  (((((o)))))
%e A298424 32  (ooooo)
%e A298424 49  ((oo)(oo))
%e A298424 64  (oooooo)
%e A298424 76  (oo(ooo))
%e A298424 86  (o(o(oo)))
%e A298424 127 ((((((o))))))
%e A298424 128 (ooooooo)
%e A298424 256 (oooooooo)
%e A298424 301 ((oo)(o(oo)))
%e A298424 424 (ooo(oooo))
%e A298424 454 (o((oo)(oo)))
%e A298424 512 (ooooooooo)
%e A298424 709 (((((((o)))))))
%e A298424 722 (o(ooo)(ooo))
%e A298424 886 (o(o(o(oo))))
%t A298424 MGtree[n_]:=If[n===1,{},MGtree/@Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A298424 soQ[n_]:=Or[n===1,SameQ@@Length/@Cases[MGtree[n],{__},{0,Infinity}]];
%t A298424 Select[Range[1000],soQ]
%Y A298424 Cf. A000081, A000598, A001190, A003238, A007097, A111299, A214577, A276625, A298422, A298423, A298426.
%K A298424 nonn
%O A298424 1,2
%A A298424 _Gus Wiseman_, Jan 19 2018