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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 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.)