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A298305 Matula-Goebel numbers of rooted trees with strictly thinning limbs. 5
1, 2, 4, 6, 8, 9, 12, 16, 18, 24, 27, 28, 32, 36, 42, 48, 52, 54, 56, 63, 64, 72, 78, 81, 84, 92, 96, 98, 104, 108, 112, 117, 126, 128, 138, 144, 147, 152, 156, 162, 168, 182, 184, 189, 192, 196, 207, 208, 216, 224, 228, 234, 243, 252, 256, 273, 276, 288, 294 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

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

LINKS

Table of n, a(n) for n=1..59.

EXAMPLE

Sequence of trees begins:

1  o

2  (o)

4  (oo)

6  (o(o))

8  (ooo)

9  ((o)(o))

12 (oo(o))

16 (oooo)

18 (o(o)(o))

24 (ooo(o))

27 ((o)(o)(o))

28 (oo(oo))

32 (ooooo)

36 (oo(o)(o))

42 (o(o)(oo))

48 (oooo(o))

52 (oo(o(o)))

54 (o(o)(o)(o))

56 (ooo(oo))

63 ((o)(o)(oo))

64 (oooooo)

72 (ooo(o)(o))

78 (o(o)(o(o)))

81 ((o)(o)(o)(o))

84 (oo(o)(oo))

92 (oo((o)(o)))

96 (ooooo(o))

98 (o(oo)(oo))

MATHEMATICA

MGtree[n_]:=If[n===1, {}, MGtree/@Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];

strthinQ[t_]:=And@@Cases[t, b_List:>Length[b]>Max@@Length/@b, {0, Infinity}];

Select[Range[200], strthinQ[MGtree[#]]&]

CROSSREFS

Cf. A000081, A007097, A061775, A111299, A124343, A124346, A214577, A276625, A290760, A291636, A298126, A298120, A298304.

Sequence in context: A337674 A324521 A146982 * A090958 A245047 A074901

Adjacent sequences:  A298302 A298303 A298304 * A298306 A298307 A298308

KEYWORD

nonn

AUTHOR

Gus Wiseman, Jan 16 2018

STATUS

approved

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Last modified December 4 13:29 EST 2021. Contains 349526 sequences. (Running on oeis4.)