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A316494
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Matula-Goebel numbers of locally disjoint rooted identity trees, meaning no branch overlaps any other branch of the same root.
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9
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1, 2, 3, 5, 6, 10, 11, 13, 15, 22, 26, 29, 30, 31, 33, 41, 47, 55, 58, 62, 66, 79, 82, 93, 94, 101, 109, 110, 113, 123, 127, 137, 141, 143, 145, 155, 158, 165, 179, 186, 202, 205, 211, 218, 226, 246, 254, 257, 271, 274, 282, 286, 290, 293, 310, 317, 327, 330
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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 prime indices are pairwise coprime, distinct, 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 identity trees preceded by their Matula-Goebel numbers begins:
1: o
2: (o)
3: ((o))
5: (((o)))
6: (o(o))
10: (o((o)))
11: ((((o))))
13: ((o(o)))
15: ((o)((o)))
22: (o(((o))))
26: (o(o(o)))
29: ((o((o))))
30: (o(o)((o)))
31: (((((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}]]]];
Select[Range[1000], Or[#==1, And[SquareFreeQ[#], Or[PrimeQ[#], CoprimeQ@@primeMS[#]], And@@#0/@primeMS[#]]]&]
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CROSSREFS
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Cf. A000081, A004111, A007097, A276625, A277098, A302696, A303362, A304713, A316467, A316471, A316474, A316495.
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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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