A298538 - OEIS

%I #5 Jan 22 2018 03:07:53

%S 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 53,59,61,64,67,71,73,79,81,83,89,97,101,103,107,109,113,121,125,127,

%U 128,131,137,139,143,149,151,157,163,167,169,173,175,179,181,187

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

%e Sequence of trees 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 11 ((((o))))

%e 13 ((o(o)))

%e 16 (oooo)

%e 17 (((oo)))

%e 19 ((ooo))

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

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

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

%e 29 ((o((o))))

%e 31 (((((o)))))

%t nn=500;

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

%t MGweight[n_]:=If[n===1,1,1+Total[MGweight/@primeMS[n]]];

%t Select[Range[nn],SameQ@@MGweight/@primeMS[#]&]

%Y Cf. A000081, A007097, A061775, A111299, A214577, A276625, A290760, A291442, A297571, A298478, A298534, A298536, A298537.

%K nonn

%O 1,2

%A _Gus Wiseman_, Jan 21 2018