A298363 Matula-Goebel numbers of rooted identity trees with thinning limbs.

1, 2, 3, 5, 6, 10, 11, 15, 22, 26, 30, 31, 33, 39, 55, 58, 62, 65, 66, 78, 87, 93, 94, 110, 127, 130, 141, 143, 145, 155, 158, 165, 174, 186, 195, 202, 235, 237, 254, 274, 282, 286, 290, 303, 310, 319, 330, 334, 341, 377, 381, 390, 395, 403, 411, 429, 435, 465

Offset

1,2

Comments

An unlabeled rooted tree has thinning limbs if its outdegrees are weakly decreasing from root to leaves.

Links

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

Formula

Intersection of A276625 and A298303.

Example

Sequence of trees begins:
1  o
2  (o)
3  ((o))
5  (((o)))
6  (o(o))
10 (o((o)))
11 ((((o))))
15 ((o)((o)))
22 (o(((o))))
26 (o(o(o)))
30 (o(o)((o)))
31 (((((o)))))
33 ((o)(((o))))
39 ((o)(o(o)))
55 (((o))(((o))))
58 (o(o((o))))
62 (o((((o)))))
65 (((o))(o(o)))
66 (o(o)(((o))))
78 (o(o)(o(o)))
87 ((o)(o((o))))
93 ((o)((((o)))))
94 (o((o)((o))))

Mathematica

MGtree[n_]:=If[n===1, {}, MGtree/@Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
idthinQ[t_]:=And@@Cases[t, b_List:>UnsameQ@@b&&Length[b]>=Max@@Length/@b, {0, Infinity}];
Select[Range[500], idthinQ[MGtree[#]]&]

Crossrefs

Cf. A000081, A004111, A007097, A061775, A111299, A124343, A124346, A214577, A276625, A277098, A290689, A290760, A298304, A298305.

Sequence in context: A322912 A072720 A325354 * A018396 A003238 A051839

Adjacent sequences: A298360 A298361 A298362 * A298364 A298365 A298366

Keyword

nonn

Author

Gus Wiseman, Jan 17 2018

Status

approved