

A331489


MatulaGoebel numbers of topologically seriesreduced rooted trees.


6



1, 2, 7, 8, 16, 19, 28, 32, 43, 53, 56, 64, 76, 98, 107, 112, 128, 131, 152, 163, 172, 196, 212, 224, 227, 256, 263, 266, 304, 311, 343, 344, 383, 392, 424, 428, 443, 448, 512, 521, 524, 532, 577, 602, 608, 613, 652, 686, 688, 719, 722, 742, 751, 784, 848, 856
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OFFSET

1,2


COMMENTS

We say that a rooted tree is topologically seriesreduced if no vertex (including the root) has degree 2.
The MatulaGoebel number of a rooted tree is the product of primes indexed by the MatulaGoebel numbers of its branches. This gives a bijective correspondence between positive integers and unlabeled rooted trees.


LINKS

Table of n, a(n) for n=1..56.
Eric Weisstein's World of Mathematics, Seriesreduced tree.
Gus Wiseman, Sequences counting seriesreduced and lonechildavoiding trees by number of vertices.


EXAMPLE

The sequence of all topologically seriesreduced rooted trees together with their MatulaGoebel numbers begins:
1: o
2: (o)
7: ((oo))
8: (ooo)
16: (oooo)
19: ((ooo))
28: (oo(oo))
32: (ooooo)
43: ((o(oo)))
53: ((oooo))
56: (ooo(oo))
64: (oooooo)
76: (oo(ooo))
98: (o(oo)(oo))
107: ((oo(oo)))
112: (oooo(oo))
128: (ooooooo)
131: ((ooooo))
152: (ooo(ooo))
163: ((o(ooo)))


MATHEMATICA

nn=1000;
primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
srQ[n_]:=Or[n==1, With[{m=primeMS[n]}, And[Length[m]>1, And@@srQ/@m]]];
Select[Range[nn], PrimeOmega[#]!=2&&And@@srQ/@primeMS[#]&]


CROSSREFS

Unlabeled rooted trees are counted by A000081.
Topologically seriesreduced trees are counted by A000014.
Topologically seriesreduced rooted trees are counted by A001679.
Labeled topologically seriesreduced trees are counted by A005512.
Labeled topologically seriesreduced rooted trees are counted by A060313.
MatulaGoebel numbers of lonechildavoiding rooted trees are A291636.
Cf. A000669, A001678, A007097, A007821, A060356, A061775, A109082, A109129, A196050, A254382, A276625, A330943, A331490.
Sequence in context: A162664 A341706 A032689 * A300476 A213037 A287343
Adjacent sequences: A331486 A331487 A331488 * A331490 A331491 A331492


KEYWORD

nonn


AUTHOR

Gus Wiseman, Jan 20 2020


STATUS

approved



