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 A316470 Matula-Goebel numbers of unlabeled rooted RPMG-trees, meaning the Matula-Goebel numbers of the branches of any non-leaf node are relatively prime. 22
 1, 2, 4, 6, 8, 12, 14, 16, 18, 24, 26, 28, 32, 36, 38, 42, 48, 52, 54, 56, 64, 72, 74, 76, 78, 84, 86, 96, 98, 104, 106, 108, 112, 114, 122, 126, 128, 144, 148, 152, 156, 162, 168, 172, 178, 182, 192, 196, 202, 208, 212, 214, 216, 222, 224, 228, 234, 244, 252 (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 it is 1 or its prime indices are relatively prime and already belong to the sequence. LINKS Table of n, a(n) for n=1..59. EXAMPLE The sequence of all RPMG-trees preceded by their Matula-Goebel numbers begins: 1: o 2: (o) 4: (oo) 6: (o(o)) 8: (ooo) 12: (oo(o)) 14: (o(oo)) 16: (oooo) 18: (o(o)(o)) 24: (ooo(o)) 26: (o(o(o))) 28: (oo(oo)) 32: (ooooo) 36: (oo(o)(o)) 38: (o(ooo)) 42: (o(o)(oo)) MATHEMATICA primeMS[n_]:=If[n===1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]]; Select[Range[1000], Or[#==1, And[GCD@@primeMS[#]==1, And@@#0/@primeMS[#]]]&] CROSSREFS Cf. A000081, A000837, A007097, A289509, A302796, A316468, A316469, A316473, A316475, A316495. Sequence in context: A254748 A217562 A088879 * A290822 A318186 A139363 Adjacent sequences: A316467 A316468 A316469 * A316471 A316472 A316473 KEYWORD nonn AUTHOR Gus Wiseman, Jul 04 2018 STATUS approved

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Last modified February 23 17:43 EST 2024. Contains 370283 sequences. (Running on oeis4.)