cp's OEIS Frontend

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.

%I A316470 #5 Jul 05 2018 07:21:12
%S A316470 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 A316470 78,84,86,96,98,104,106,108,112,114,122,126,128,144,148,152,156,162,
%U A316470 168,172,178,182,192,196,202,208,212,214,216,222,224,228,234,244,252
%N 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.
%C A316470 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 A316470 The sequence of all RPMG-trees preceded by their Matula-Goebel numbers begins:
%e A316470    1: o
%e A316470    2: (o)
%e A316470    4: (oo)
%e A316470    6: (o(o))
%e A316470    8: (ooo)
%e A316470   12: (oo(o))
%e A316470   14: (o(oo))
%e A316470   16: (oooo)
%e A316470   18: (o(o)(o))
%e A316470   24: (ooo(o))
%e A316470   26: (o(o(o)))
%e A316470   28: (oo(oo))
%e A316470   32: (ooooo)
%e A316470   36: (oo(o)(o))
%e A316470   38: (o(ooo))
%e A316470   42: (o(o)(oo))
%t A316470 primeMS[n_]:=If[n===1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A316470 Select[Range[1000],Or[#==1,And[GCD@@primeMS[#]==1,And@@#0/@primeMS[#]]]&]
%Y A316470 Cf. A000081, A000837, A007097, A289509, A302796, A316468, A316469, A316473, A316475, A316495.
%K A316470 nonn
%O A316470 1,2
%A A316470 _Gus Wiseman_, Jul 04 2018