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 A316468 Matula-Goebel numbers of locally stable rooted trees, meaning no branch is a submultiset of any other branch of the same root. 9
 1, 2, 3, 4, 5, 7, 8, 9, 11, 15, 16, 17, 19, 23, 25, 27, 31, 32, 33, 35, 45, 47, 49, 51, 53, 55, 59, 64, 67, 69, 75, 77, 81, 83, 85, 93, 95, 97, 99, 103, 119, 121, 125, 127, 128, 131, 135, 137, 141, 149, 153, 155, 161, 165, 175, 177, 187, 197, 201, 207, 209 (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 is in the sequence iff its distinct prime indices are pairwise indivisible and already belong to the sequence. LINKS EXAMPLE Sequence of locally stable rooted trees preceded by their Matula-Goebel numbers begins:    1: o    2: (o)    3: ((o))    4: (oo)    5: (((o)))    7: ((oo))    8: (ooo)    9: ((o)(o))   11: ((((o))))   15: ((o)((o)))   16: (oooo)   17: (((oo)))   19: ((ooo))   23: (((o)(o)))   25: (((o))((o)))   27: ((o)(o)(o))   31: (((((o))))) MATHEMATICA primeMS[n_]:=If[n===1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]]; Select[Range[100], Or[#==1, And[Select[Tuples[primeMS[#], 2], UnsameQ@@#&&Divisible@@#&]=={}, And@@#0/@primeMS[#]]]&] CROSSREFS Cf. A000081, A004111, A007097, A112798, A277098, A285572, A285573, A303362, A304713, A316467, A316470, A316473, A316475, A316476, A316495. Sequence in context: A282136 A153730 A140691 * A099627 A184155 A318612 Adjacent sequences:  A316465 A316466 A316467 * A316469 A316470 A316471 KEYWORD nonn AUTHOR Gus Wiseman, Jul 04 2018 STATUS approved

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Last modified February 19 07:51 EST 2019. Contains 320309 sequences. (Running on oeis4.)