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Matula-Goebel numbers of unlabeled rooted RPMG-trees, meaning the Matula-Goebel numbers of the branches of any non-leaf node are relatively prime.
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%I #5 Jul 05 2018 07:21:12

%S 1,2,4,6,8,12,14,16,18,24,26,28,32,36,38,42,48,52,54,56,64,72,74,76,

%T 78,84,86,96,98,104,106,108,112,114,122,126,128,144,148,152,156,162,

%U 168,172,178,182,192,196,202,208,212,214,216,222,224,228,234,244,252

%N Matula-Goebel numbers of unlabeled rooted RPMG-trees, meaning the Matula-Goebel numbers of the branches of any non-leaf node are relatively prime.

%C 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.

%e The sequence of all RPMG-trees preceded by their Matula-Goebel numbers begins:

%e 1: o

%e 2: (o)

%e 4: (oo)

%e 6: (o(o))

%e 8: (ooo)

%e 12: (oo(o))

%e 14: (o(oo))

%e 16: (oooo)

%e 18: (o(o)(o))

%e 24: (ooo(o))

%e 26: (o(o(o)))

%e 28: (oo(oo))

%e 32: (ooooo)

%e 36: (oo(o)(o))

%e 38: (o(ooo))

%e 42: (o(o)(oo))

%t primeMS[n_]:=If[n===1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];

%t Select[Range[1000],Or[#==1,And[GCD@@primeMS[#]==1,And@@#0/@primeMS[#]]]&]

%Y Cf. A000081, A000837, A007097, A289509, A302796, A316468, A316469, A316473, A316475, A316495.

%K nonn

%O 1,2

%A _Gus Wiseman_, Jul 04 2018