cp's OEIS Frontend

A316469 Matula-Goebel numbers of unlabeled rooted identity RPMG-trees, meaning the Matula-Goebel numbers of the branches of any non-leaf node are relatively prime.

%I A316469 #5 Jul 05 2018 07:21:05
%S A316469 1,2,6,26,78,202,606,794,2382,2462,2626,7386,7878,8914,10322,12178,
%T A316469 26742,30966,32006,36534,42374,43954,47206,80194,96018,115882,127122,
%U A316469 131862,141618,149782,158314,160978,184622,217058,240582,248662,260422,347646,449346
%N A316469 Matula-Goebel numbers of unlabeled rooted identity RPMG-trees, meaning the Matula-Goebel numbers of the branches of any non-leaf node are relatively prime.
%C A316469 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 distinct, relatively prime, and already belong to the sequence.
%e A316469 78 = prime(1)*prime(2)*prime(6) belongs to the sequence because the indices {1,2,6} are relatively prime, distinct, and already belong to the sequence.
%e A316469 The sequence of all identity RPMG-trees preceded by their Matula-Goebel numbers begins:
%e A316469      1: o
%e A316469      2: (o)
%e A316469      6: (o(o))
%e A316469     26: (o(o(o)))
%e A316469     78: (o(o)(o(o)))
%e A316469    202: (o(o(o(o))))
%e A316469    606: (o(o)(o(o(o))))
%e A316469    794: (o(o(o)(o(o))))
%e A316469   2382: (o(o)(o(o)(o(o))))
%e A316469   2462: (o(o(o(o(o)))))
%e A316469   2626: (o(o(o))(o(o(o))))
%e A316469   7386: (o(o)(o(o(o(o)))))
%e A316469   7878: (o(o)(o(o))(o(o(o))))
%t A316469 primeMS[n_]:=If[n===1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A316469 Select[Range[1000],Or[#==1,And[SquareFreeQ[#],GCD@@primeMS[#]==1,And@@#0/@primeMS[#]]]&]
%Y A316469 Cf. A000081, A000837, A004111, A007097, A078374, A276625, A289509, A302696, A302796, A316467, A316470, A316471, A316474, A316494.
%K A316469 nonn
%O A316469 1,2
%A A316469 _Gus Wiseman_, Jul 04 2018