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A298536 Matula-Goebel numbers of rooted trees such that every branch of the root has a different number of leaves.

%I A298536 #6 Jan 22 2018 03:07:40
%S A298536 1,2,3,5,7,11,13,14,17,19,21,23,26,29,31,34,35,37,38,39,41,43,46,47,
%T A298536 51,53,57,58,59,61,65,67,69,71,73,74,77,79,82,83,85,86,87,89,94,95,97,
%U A298536 101,103,106,107,109,111,113,115,118,122,123,127,129,131,133
%N A298536 Matula-Goebel numbers of rooted trees such that every branch of the root has a different number of leaves.
%e A298536 Sequence of trees begins:
%e A298536 1  o
%e A298536 2  (o)
%e A298536 3  ((o))
%e A298536 5  (((o)))
%e A298536 7  ((oo))
%e A298536 11 ((((o))))
%e A298536 13 ((o(o)))
%e A298536 14 (o(oo))
%e A298536 17 (((oo)))
%e A298536 19 ((ooo))
%e A298536 21 ((o)(oo))
%e A298536 23 (((o)(o)))
%e A298536 26 (o(o(o)))
%e A298536 29 ((o((o))))
%e A298536 31 (((((o)))))
%e A298536 34 (o((oo)))
%e A298536 35 (((o))(oo))
%e A298536 37 ((oo(o)))
%e A298536 38 (o(ooo))
%e A298536 39 ((o)(o(o)))
%e A298536 41 (((o(o))))
%e A298536 43 ((o(oo)))
%e A298536 46 (o((o)(o)))
%e A298536 47 (((o)((o))))
%t A298536 nn=2000;
%t A298536 primeMS[n_]:=If[n===1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A298536 leafcount[n_]:=If[n===1,1,With[{m=primeMS[n]},If[Length[m]===1,leafcount[First[m]],Total[leafcount/@m]]]];
%t A298536 Select[Range[nn],UnsameQ@@leafcount/@primeMS[#]&]
%Y A298536 Cf. A000081, A007097, A061775, A111299, A214577, A276625, A290689, A290760, A291442, A298534, A298535.
%K A298536 nonn
%O A298536 1,2
%A A298536 _Gus Wiseman_, Jan 20 2018