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A298120 Matula-Goebel numbers of rooted trees in which all positive outdegrees are odd.

%I A298120 #10 Oct 23 2021 21:17:42
%S A298120 1,2,3,5,8,11,12,18,19,20,27,30,31,32,37,44,45,48,50,61,66,67,71,72,
%T A298120 75,76,80,99,103,108,110,113,114,120,124,125,127,128,131,148,157,162,
%U A298120 165,171,176,180,186,190,192,193,197,200,222,223,229,242,243,244,264
%N A298120 Matula-Goebel numbers of rooted trees in which all positive outdegrees are odd.
%H A298120 <a href="/index/Mat#matula">Index entries for sequences related to Matula-Goebel numbers</a>
%e A298120 Sequence of trees begins:
%e A298120 1  o
%e A298120 2  (o)
%e A298120 3  ((o))
%e A298120 5  (((o)))
%e A298120 8  (ooo)
%e A298120 11 ((((o))))
%e A298120 12 (oo(o))
%e A298120 18 (o(o)(o))
%e A298120 19 ((ooo))
%e A298120 20 (oo((o)))
%e A298120 27 ((o)(o)(o))
%e A298120 30 (o(o)((o)))
%e A298120 31 (((((o)))))
%e A298120 32 (ooooo)
%e A298120 37 ((oo(o)))
%e A298120 44 (oo(((o))))
%e A298120 45 ((o)(o)((o)))
%e A298120 48 (oooo(o))
%e A298120 50 (o((o))((o)))
%t A298120 primeMS[n_]:=If[n===1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A298120 otQ[n_]:=Or[n===1,With[{m=primeMS[n]},OddQ@Length@m&&And@@otQ/@m]];
%t A298120 Select[Range[1000],otQ]
%Y A298120 Cf. A000081, A007097, A026424, A061775, A214577, A276625, A277098, A290760, A291441, A291442, A291636, A297571, A298118.
%K A298120 nonn
%O A298120 1,2
%A A298120 _Gus Wiseman_, Jan 12 2018