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A303026 Matula-Goebel numbers of series-reduced anti-binary (no unary or binary branchings) rooted trees.

%I A303026 #9 Aug 16 2018 08:51:36
%S A303026 1,8,16,32,64,76,128,152,212,256,304,424,512,524,608,722,848,1024,
%T A303026 1048,1216,1244,1444,1532,1696,2014,2048,2096,2432,2488,2876,2888,
%U A303026 3064,3392,3524,4028,4096,4192,4864,4976,4978,5204,5618,5752,5776,6128,6476,6784
%N A303026 Matula-Goebel numbers of series-reduced anti-binary (no unary or binary branchings) rooted trees.
%e A303026 The sequence of series-reduced anti-binary rooted trees together with their Matula-Goebel numbers begins:
%e A303026      1: o
%e A303026      8: (ooo)
%e A303026     16: (oooo)
%e A303026     32: (ooooo)
%e A303026     64: (oooooo)
%e A303026     76: (oo(ooo))
%e A303026    128: (ooooooo)
%e A303026    152: (ooo(ooo))
%e A303026    212: (oo(oooo))
%e A303026    256: (oooooooo)
%e A303026    304: (oooo(ooo))
%e A303026    424: (ooo(oooo))
%e A303026    512: (ooooooooo)
%e A303026    524: (oo(ooooo))
%e A303026    608: (ooooo(ooo))
%e A303026    722: (o(ooo)(ooo))
%e A303026    848: (oooo(oooo))
%e A303026   1024: (oooooooooo)
%e A303026   1048: (ooo(ooooo))
%e A303026   1216: (oooooo(ooo))
%e A303026   1244: (oo(oooooo))
%e A303026   1444: (oo(ooo)(ooo))
%e A303026   1532: (oo(oo(ooo)))
%e A303026   1696: (ooooo(oooo))
%e A303026   2014: (o(ooo)(oooo))
%e A303026   2048: (ooooooooooo)
%t A303026 azQ[n_]:=Or[n==1,And[PrimeOmega[n]>2,And@@Cases[FactorInteger[n],{p_,_}:>azQ[PrimePi[p]]]]]
%t A303026 Select[Range[1000],azQ]
%Y A303026 Cf. A000081, A000598, A001190, A001678, A007097, A061775, A102403, A111299, A292050, A298422, A298424.
%Y A303026 Cf. A303022, A303023, A303024, A303025, A303027.
%K A303026 nonn
%O A303026 1,2
%A A303026 _Gus Wiseman_, Aug 15 2018