A324928 - OEIS

%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