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 A316467 Matula-Goebel numbers of locally stable rooted identity trees, meaning no branch is a subset of any other branch of the same root. 9
 1, 2, 3, 5, 11, 15, 31, 33, 47, 55, 93, 127, 137, 141, 155, 165, 211, 257, 341, 381, 411, 465, 487, 633, 635, 709, 771, 773, 811, 907, 977, 1023, 1055, 1285, 1297, 1397, 1457, 1461, 1507, 1621, 1705, 1905, 2127, 2293, 2319, 2321, 2433, 2621, 2721, 2833, 2931 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS A prime index of n is a number m such that prime(m) divides n. A number belongs to this sequence iff it is squarefree, its distinct prime indices are pairwise indivisible, and its prime indices also belong to this sequence. LINKS EXAMPLE 165 = prime(2)*prime(3)*prime(5) belongs to the sequence because it is squarefree, the indices {2,3,5} are pairwise indivisible, and each of them already belongs to the sequence. Sequence of locally stable rooted identity trees preceded by their Matula-Goebel numbers begins:     1: o     2: (o)     3: ((o))     5: (((o)))    11: ((((o))))    15: ((o)((o)))    31: (((((o)))))    33: ((o)(((o))))    47: (((o)((o))))    55: (((o))(((o))))    93: ((o)((((o)))))   127: ((((((o))))))   137: (((o)(((o)))))   141: ((o)((o)((o))))   155: (((o))((((o)))))   165: ((o)((o))(((o)))) MATHEMATICA primeMS[n_]:=If[n===1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]]; ain[n_]:=And[Select[Tuples[primeMS[n], 2], UnsameQ@@#&&Divisible@@#&]=={}, SquareFreeQ[n], And@@ain/@primeMS[n]]; Select[Range, ain] CROSSREFS Cf. A000081, A004111, A007097, A276625, A277098, A285572, A285573, A302796, A303362, A304713, A316468, A316469, A316471, A316474, A316476, A316494. Sequence in context: A004680 A230147 A324855 * A282238 A004690 A001882 Adjacent sequences:  A316464 A316465 A316466 * A316468 A316469 A316470 KEYWORD nonn AUTHOR Gus Wiseman, Jul 04 2018 STATUS approved

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Last modified April 4 05:34 EDT 2020. Contains 333212 sequences. (Running on oeis4.)