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

1,2

Links

Table of n, a(n) for n=1..58.

Example

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)))

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]

Crossrefs

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

Sequence in context: A303024 A070223 A298120 * A117725 A106637 A246361

Adjacent sequences: A298202 A298203 A298204 * A298206 A298207 A298208

Keyword

nonn

Author

Gus Wiseman, Jan 14 2018

Status

approved