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