cp's OEIS Frontend

A298538 Matula-Goebel numbers of rooted trees such that every branch of the root has the same number of nodes.

%I A298538 #5 Jan 22 2018 03:07:53
%S A298538 1,2,3,4,5,7,8,9,11,13,16,17,19,23,25,27,29,31,32,35,37,41,43,47,49,
%T A298538 53,59,61,64,67,71,73,79,81,83,89,97,101,103,107,109,113,121,125,127,
%U A298538 128,131,137,139,143,149,151,157,163,167,169,173,175,179,181,187
%N A298538 Matula-Goebel numbers of rooted trees such that every branch of the root has the same number of nodes.
%e A298538 Sequence of trees begins:
%e A298538 1  o
%e A298538 2  (o)
%e A298538 3  ((o))
%e A298538 4  (oo)
%e A298538 5  (((o)))
%e A298538 7  ((oo))
%e A298538 8  (ooo)
%e A298538 9  ((o)(o))
%e A298538 11 ((((o))))
%e A298538 13 ((o(o)))
%e A298538 16 (oooo)
%e A298538 17 (((oo)))
%e A298538 19 ((ooo))
%e A298538 23 (((o)(o)))
%e A298538 25 (((o))((o)))
%e A298538 27 ((o)(o)(o))
%e A298538 29 ((o((o))))
%e A298538 31 (((((o)))))
%t A298538 nn=500;
%t A298538 primeMS[n_]:=If[n===1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A298538 MGweight[n_]:=If[n===1,1,1+Total[MGweight/@primeMS[n]]];
%t A298538 Select[Range[nn],SameQ@@MGweight/@primeMS[#]&]
%Y A298538 Cf. A000081, A007097, A061775, A111299, A214577, A276625, A290760, A291442, A297571, A298478, A298534, A298536, A298537.
%K A298538 nonn
%O A298538 1,2
%A A298538 _Gus Wiseman_, Jan 21 2018