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

1, 2, 3, 5, 8, 11, 12, 18, 19, 20, 27, 30, 31, 37, 44, 45, 50, 61, 66, 67, 71, 75, 76, 99, 103, 110, 113, 114, 124, 125, 127, 148, 157, 165, 171, 186, 190, 193, 197, 222, 229, 242, 244, 268, 275, 279, 283, 284, 285, 310, 317, 331, 333, 353, 363, 366, 370, 379

Offset: 1

Author

Gus Wiseman, Jan 14 2018

Keywords

• nonn

Examples

			Sequence of rooted trees begins:
1  o
2  (o)
3  ((o))
5  (((o)))
8  (ooo)
11 ((((o))))
12 (oo(o))
18 (o(o)(o))
19 ((ooo))
20 (oo((o)))
27 ((o)(o)(o))
30 (o(o)((o)))
31 (((((o)))))
37 ((oo(o)))
44 (oo(((o))))
45 ((o)(o)((o)))
50 (o((o))((o)))
		

Crossrefs

Cf. A000081, A000598, A014591, A026424, A032305, A061775, A111299, A276625, A292050, A295461, A297571, A298126, A298118, A298120, A298204, A298207.

Programs

Mathematica

primeMS[n_]:=If[n===1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
stQ[n_]:=Or[n===1,With[{m=primeMS[n]},MemberQ[{1,3},Length[m]]&&And@@stQ/@m]];
Select[Range[10000],stQ]