cp's OEIS Frontend

A298534 Matula-Goebel numbers of rooted trees such that every branch of the root has the same number of leaves.

%I A298534 #7 Jan 22 2018 03:07:29
%S A298534 1,2,3,4,5,6,7,8,9,10,11,12,13,15,16,17,18,19,20,22,23,24,25,27,29,30,
%T A298534 31,32,33,36,37,40,41,43,44,45,47,48,49,50,53,54,55,59,60,61,62,64,66,
%U A298534 67,71,72,73,75,79,80,81,83,88,89,90,91,93,96,97,99,100
%N A298534 Matula-Goebel numbers of rooted trees such that every branch of the root has the same number of leaves.
%e A298534 Sequence of trees begins:
%e A298534 1  o
%e A298534 2  (o)
%e A298534 3  ((o))
%e A298534 4  (oo)
%e A298534 5  (((o)))
%e A298534 6  (o(o))
%e A298534 7  ((oo))
%e A298534 8  (ooo)
%e A298534 9  ((o)(o))
%e A298534 10 (o((o)))
%e A298534 11 ((((o))))
%e A298534 12 (oo(o))
%e A298534 13 ((o(o)))
%e A298534 15 ((o)((o)))
%e A298534 16 (oooo)
%e A298534 17 (((oo)))
%e A298534 18 (o(o)(o))
%e A298534 19 ((ooo))
%e A298534 20 (oo((o)))
%e A298534 22 (o(((o))))
%e A298534 23 (((o)(o)))
%e A298534 24 (ooo(o))
%e A298534 25 (((o))((o)))
%e A298534 27 ((o)(o)(o))
%e A298534 29 ((o((o))))
%e A298534 30 (o(o)((o)))
%t A298534 nn=2000;
%t A298534 primeMS[n_]:=If[n===1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A298534 leafcount[n_]:=If[n===1,1,With[{m=primeMS[n]},If[Length[m]===1,leafcount[First[m]],Total[leafcount/@m]]]];
%t A298534 Select[Range[nn],SameQ@@leafcount/@primeMS[#]&]
%Y A298534 Cf. A000081, A007097, A061775, A111299, A214577, A276625, A290760, A290822, A291442, A298533, A298536.
%K A298534 nonn
%O A298534 1,2
%A A298534 _Gus Wiseman_, Jan 20 2018