cp's OEIS Frontend

A298205 Matula-Goebel numbers of rooted trees in which all outdegrees are either 0, 1, or 3.

%I A298205 #6 Jan 17 2018 04:28:29
%S A298205 1,2,3,5,8,11,12,18,19,20,27,30,31,37,44,45,50,61,66,67,71,75,76,99,
%T A298205 103,110,113,114,124,125,127,148,157,165,171,186,190,193,197,222,229,
%U A298205 242,244,268,275,279,283,284,285,310,317,331,333,353,363,366,370,379
%N A298205 Matula-Goebel numbers of rooted trees in which all outdegrees are either 0, 1, or 3.
%e A298205 Sequence of rooted trees begins:
%e A298205 1  o
%e A298205 2  (o)
%e A298205 3  ((o))
%e A298205 5  (((o)))
%e A298205 8  (ooo)
%e A298205 11 ((((o))))
%e A298205 12 (oo(o))
%e A298205 18 (o(o)(o))
%e A298205 19 ((ooo))
%e A298205 20 (oo((o)))
%e A298205 27 ((o)(o)(o))
%e A298205 30 (o(o)((o)))
%e A298205 31 (((((o)))))
%e A298205 37 ((oo(o)))
%e A298205 44 (oo(((o))))
%e A298205 45 ((o)(o)((o)))
%e A298205 50 (o((o))((o)))
%t A298205 primeMS[n_]:=If[n===1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A298205 stQ[n_]:=Or[n===1,With[{m=primeMS[n]},MemberQ[{1,3},Length[m]]&&And@@stQ/@m]];
%t A298205 Select[Range[10000],stQ]
%Y A298205 Cf. A000081, A000598, A014591, A026424, A032305, A061775, A111299, A276625, A292050, A295461, A297571, A298126, A298118, A298120, A298204, A298207.
%K A298205 nonn
%O A298205 1,2
%A A298205 _Gus Wiseman_, Jan 14 2018