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A324928 Matula-Goebel numbers of rooted trees of depth 3.

%I A324928 #5 Mar 21 2019 17:22:13
%S A324928 5,10,13,15,17,20,23,25,26,30,34,35,37,39,40,43,45,46,50,51,52,60,61,
%T A324928 65,67,68,69,70,73,74,75,78,80,85,86,89,90,91,92,95,100,102,103,104,
%U A324928 105,107,111,115,117,119,120,122,125,129,130,134,135,136,138,140
%N A324928 Matula-Goebel numbers of rooted trees of depth 3.
%C A324928 Numbers n such that A109082(n) = 3.
%e A324928 The sequence of all rooted trees of depth 3 together with their Matula-Goebel numbers begins:
%e A324928    5: (((o)))
%e A324928   10: (o((o)))
%e A324928   13: ((o(o)))
%e A324928   15: ((o)((o)))
%e A324928   17: (((oo)))
%e A324928   20: (oo((o)))
%e A324928   23: (((o)(o)))
%e A324928   25: (((o))((o)))
%e A324928   26: (o(o(o)))
%e A324928   30: (o(o)((o)))
%e A324928   34: (o((oo)))
%e A324928   35: (((o))(oo))
%e A324928   37: ((oo(o)))
%e A324928   39: ((o)(o(o)))
%e A324928   40: (ooo((o)))
%e A324928   43: ((o(oo)))
%e A324928   45: ((o)(o)((o)))
%e A324928   46: (o((o)(o)))
%e A324928   50: (o((o))((o)))
%e A324928   51: ((o)((oo)))
%e A324928   52: (oo(o(o)))
%e A324928   60: (oo(o)((o)))
%t A324928 Select[Range[100],Length[NestWhileList[Times@@PrimePi/@FactorInteger[#][[All,1]]&,#,#>1&]]-1==3&]
%Y A324928 Cf. A000081, A003963, A007097, A102378, A318400, A324927, A324930.
%K A324928 nonn
%O A324928 1,1
%A A324928 _Gus Wiseman_, Mar 21 2019