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