cp's OEIS Frontend

A324968 Matula-Goebel numbers of rooted identity trees whose non-leaf terminal subtrees are all different.

%I A324968 #6 Mar 22 2019 00:33:28
%S A324968 1,2,3,5,6,10,11,13,22,26,29,31,41,58,62,79,82,101,109,127,158,179,
%T A324968 202,218,254,271,293,358,401,421,542,547,586,599,709,802,842,929,1063,
%U A324968 1094,1198,1231,1361,1418,1609,1741,1858,1913,2126,2411,2462,2722,2749
%N A324968 Matula-Goebel numbers of rooted identity trees whose non-leaf terminal subtrees are all different.
%C A324968 A rooted identity tree is an unlabeled rooted tree with no repeated branches directly under the same root. This sequence ranks rooted identity trees satisfying the additional condition that all non-leaf terminal subtrees are different.
%H A324968 Gus Wiseman, <a href="/A324968/a324968.png">The first 36 trees together with their Matula-Goebel numbers</a>.
%F A324968 Intersection of A324935 and A276625.
%e A324968 The sequence of trees together with the Matula-Goebel numbers begins:
%e A324968     1: o
%e A324968     2: (o)
%e A324968     3: ((o))
%e A324968     5: (((o)))
%e A324968     6: (o(o))
%e A324968    10: (o((o)))
%e A324968    11: ((((o))))
%e A324968    13: ((o(o)))
%e A324968    22: (o(((o))))
%e A324968    26: (o(o(o)))
%e A324968    29: ((o((o))))
%e A324968    31: (((((o)))))
%e A324968    41: (((o(o))))
%e A324968    58: (o(o((o))))
%e A324968    62: (o((((o)))))
%e A324968    79: ((o(((o)))))
%e A324968    82: (o((o(o))))
%e A324968   101: ((o(o(o))))
%e A324968   109: (((o((o)))))
%e A324968   127: ((((((o))))))
%t A324968 mgtree[n_Integer]:=If[n==1,{},mgtree/@Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A324968 Select[Range[100],And[And@@Cases[mgtree[#],q:{__}:>UnsameQ@@q,{0,Infinity}],UnsameQ@@Cases[mgtree[#],{__},{0,Infinity}]]&]
%Y A324968 Cf. A000081, A004111, A007097, A196050, A276625, A317713, A324850, A324923, A324935, A324936, A324969, A324970, A324978.
%K A324968 nonn
%O A324968 1,2
%A A324968 _Gus Wiseman_, Mar 21 2019