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A316495
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Matula-Goebel numbers of locally disjoint unlabeled rooted trees, meaning no branch overlaps any other (unequal) branch of the same root.
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25
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1, 2, 3, 4, 5, 6, 7, 8, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 22, 24, 26, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 40, 41, 43, 44, 45, 47, 48, 50, 51, 52, 53, 54, 55, 56, 58, 59, 60, 61, 62, 64, 66, 67, 68, 70, 71, 72, 74, 75, 76, 77, 79, 80, 82, 85
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OFFSET
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1,2
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COMMENTS
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A prime index of n is a number m such that prime(m) divides n. A number is in the sequence iff either it is equal to 1, it is a prime number whose prime index already belongs to the sequence, or its distinct prime indices are pairwise coprime and already belong to the sequence.
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LINKS
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EXAMPLE
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The sequence of all locally disjoint rooted trees preceded by their Matula-Goebel numbers begins:
1: o
2: (o)
3: ((o))
4: (oo)
5: (((o)))
6: (o(o))
7: ((oo))
8: (ooo)
10: (o((o)))
11: ((((o))))
12: (oo(o))
13: ((o(o)))
14: (o(oo))
15: ((o)((o)))
16: (oooo)
17: (((oo)))
18: (o(o)(o))
19: ((ooo))
20: (oo((o)))
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MATHEMATICA
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primeMS[n_]:=If[n===1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
go[n_]:=Or[n==1, And[Or[PrimeQ[n], CoprimeQ@@Union[primeMS[n]]], And@@go/@primeMS[n]]];
Select[Range[100], go]
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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