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Matula-Goebel numbers of rooted trees where the branches of no non-leaf branch of any terminal subtree form a submultiset of the branches of the same subtree.
3

%I #6 Mar 19 2019 07:15:27

%S 1,2,3,4,5,7,8,9,10,11,14,16,17,19,20,21,22,23,25,27,29,31,32,33,34,

%T 35,38,40,43,44,46,49,50,51,53,57,58,59,62,63,64,67,68,69,70,71,73,76,

%U 77,79,80,81,83,85,86,87,88,92,93,95,97,98,99,100,103,106

%N Matula-Goebel numbers of rooted trees where the branches of no non-leaf branch of any terminal subtree form a submultiset of the branches of the same subtree.

%H Gus Wiseman, <a href="/A324845/a324845.png">The sequence of rooted trees whose Matula-Goebel numbers belong to A324845</a>.

%e The sequence of terms together with their Matula-Goebel numbers begins:

%e 1: o

%e 2: (o)

%e 3: ((o))

%e 4: (oo)

%e 5: (((o)))

%e 7: ((oo))

%e 8: (ooo)

%e 9: ((o)(o))

%e 10: (o((o)))

%e 11: ((((o))))

%e 14: (o(oo))

%e 16: (oooo)

%e 17: (((oo)))

%e 19: ((ooo))

%e 20: (oo((o)))

%e 21: ((o)(oo))

%e 22: (o(((o))))

%e 23: (((o)(o)))

%e 25: (((o))((o)))

%e 27: ((o)(o)(o))

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

%t qaQ[n_]:=And[And@@Table[!Divisible[n,x],{x,DeleteCases[primeMS[n],1]}],And@@qaQ/@primeMS[n]];

%t Select[Range[100],qaQ]

%Y Cf. A000081, A007097, A290822, A306844, A318186.

%Y Cf. A324694, A324738, A324744, A324749, A324754, A324759, A324765, A324768, A324838, A324842, A324844, A324846, A324847, A324849.

%K nonn

%O 1,2

%A _Gus Wiseman_, Mar 18 2019