

A331873


MatulaGoebel numbers of semilonechildavoiding locally disjoint rooted trees.


14



1, 2, 4, 6, 8, 9, 12, 14, 16, 18, 24, 26, 27, 28, 32, 36, 38, 46, 48, 49, 52, 54, 56, 64, 69, 72, 74, 76, 81, 86, 92, 96, 98, 104, 106, 108, 112, 122, 128, 138, 144, 148, 152, 161, 162, 169, 172, 178, 184, 192, 196, 202, 206, 207, 208, 212, 214, 216, 224, 243
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OFFSET

1,2


COMMENTS

First differs from A331936 in having 69, the MatulaGoebel number of the tree ((o)((o)(o))).
A rooted tree is semilonechildavoiding if there are no vertices with exactly one child unless the child is an endpoint/leaf.
Locally disjoint means no child of any vertex has branches overlapping the branches of any other (inequivalent) child of the same vertex.
The MatulaGoebel number of a rooted tree is the product of primes indexed by the MatulaGoebel numbers of the branches of its root, which gives a bijective correspondence between positive integers and unlabeled rooted trees.
Consists of one, two, and all nonprime numbers whose distinct prime indices are pairwise coprime and already belong to the sequence, where a singleton is always considered to be pairwise coprime. A prime index of n is a number m such that prime(m) divides n.


LINKS



EXAMPLE

The sequence of all semilonechildavoiding locally disjoint rooted trees together with their MatulaGoebel numbers begins:
1: o
2: (o)
4: (oo)
6: (o(o))
8: (ooo)
9: ((o)(o))
12: (oo(o))
14: (o(oo))
16: (oooo)
18: (o(o)(o))
24: (ooo(o))
26: (o(o(o)))
27: ((o)(o)(o))
28: (oo(oo))
32: (ooooo)
36: (oo(o)(o))
38: (o(ooo))
46: (o((o)(o)))
48: (oooo(o))
49: ((oo)(oo))


MATHEMATICA

msQ[n_]:=n==1n==2!PrimeQ[n]&&(PrimePowerQ[n]CoprimeQ@@PrimePi/@First/@FactorInteger[n])&&And@@msQ/@PrimePi/@First/@FactorInteger[n];
Select[Range[100], msQ]


CROSSREFS

Not requiring lonechildavoidance gives A316495.
The semiidentity tree case is A331681.
The nonsemi version (i.e., not containing 2) is A331871.
These trees counted by vertices are A331872.
These trees counted by leaves are A331874.
Not requiring local disjointness gives A331935.
Cf. A007097, A050381, A061775, A196050, A291636, A302696, A316473, A316696, A316697, A331680, A331682, A331683, A331687, A331934.


KEYWORD

nonn


AUTHOR



STATUS

approved



