cp's OEIS Frontend

A316503 Matula-Goebel numbers of unlabeled rooted identity trees with n nodes in which the branches of any node with more than one branch have empty intersection.

%I A316503 #5 Jul 05 2018 07:21:44
%S A316503 1,2,3,5,6,10,11,13,15,22,26,29,30,31,33,41,47,55,58,62,66,78,79,82,
%T A316503 93,94,101,109,110,113,123,127,130,137,141,143,145,155,158,165,174,
%U A316503 179,186,195,202,205,211,218,226,246,254,257,271,274,282,286,290,293
%N A316503 Matula-Goebel numbers of unlabeled rooted identity trees with n nodes in which the branches of any node with more than one branch have empty intersection.
%e A316503 Sequence of rooted identity trees preceded by their Matula-Goebel numbers begins:
%e A316503    1: o
%e A316503    2: (o)
%e A316503    3: ((o))
%e A316503    5: (((o)))
%e A316503    6: (o(o))
%e A316503   10: (o((o)))
%e A316503   11: ((((o))))
%e A316503   13: ((o(o)))
%e A316503   15: ((o)((o)))
%e A316503   22: (o(((o))))
%e A316503   26: (o(o(o)))
%e A316503   29: ((o((o))))
%e A316503   30: (o(o)((o)))
%e A316503   31: (((((o)))))
%t A316503 primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A316503 Select[Range[100],Or[#==1,And[SquareFreeQ[#],Or[PrimeQ[#],GCD@@primeMS[#]==1],And@@#0/@primeMS[#]]]&]
%Y A316503 Cf. A000081, A000837, A004111, A007097, A078374, A276625, A289509, A302796, A316467, A316470, A316494, A316502.
%K A316503 nonn
%O A316503 1,2
%A A316503 _Gus Wiseman_, Jul 05 2018