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Matula-Goebel numbers of rooted trees in which all positive outdegrees are odd.
9

%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