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 A319270 Numbers that are 1 or whose prime indices are relatively prime and belong to the sequence, and whose prime multiplicities are also relatively prime. 1
 1, 2, 6, 12, 18, 24, 26, 48, 52, 54, 72, 74, 78, 96, 104, 108, 122, 148, 156, 162, 178, 192, 202, 208, 222, 234, 244, 288, 296, 312, 338, 356, 366, 384, 404, 416, 432, 444, 446, 468, 478, 486, 488, 502, 534, 592, 606, 624, 648, 666, 702, 712, 718, 732, 746 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Also Matula-Goebel numbers of series-reduced locally non-intersecting aperiodic rooted trees. LINKS EXAMPLE The sequence of Matula-Goebel trees of elements of this sequence begins:    1: o    2: (o)    6: (o(o))   12: (oo(o))   18: (o(o)(o))   24: (ooo(o))   26: (o(o(o)))   48: (oooo(o))   52: (oo(o(o)))   54: (o(o)(o)(o))   72: (ooo(o)(o))   74: (o(oo(o)))   78: (o(o)(o(o)))   96: (ooooo(o)) MATHEMATICA primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]]; ain[n_]:=Or[n==1, And[GCD@@primeMS[n]==1, GCD@@Length/@Split[primeMS[n]]==1, And@@ain/@primeMS[n]]]; Select[Range[100], ain] CROSSREFS Cf. A000081, A007097, A061775, A276625, A298748, A301700, A303431, A316470, A319271. Sequence in context: A263082 A043343 A066080 * A071707 A069087 A304450 Adjacent sequences:  A319267 A319268 A319269 * A319271 A319272 A319273 KEYWORD nonn AUTHOR Gus Wiseman, Sep 16 2018 STATUS approved

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Last modified March 18 13:47 EDT 2019. Contains 321289 sequences. (Running on oeis4.)