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%I #5 May 13 2019 08:11:58
%S 1,2,3,4,5,6,8,9,10,11,12,15,16,18,20,22,24,25,27,30,31,32,33,36,40,
%T 44,45,48,50,54,55,60,62,64,66,72,75,80,81,88,90,93,96,99,100,108,110,
%U 120,121,124,125,127,128,132,135,144,150,155,160,162,165,176
%N Matula-Goebel numbers of not necessarily regular rooted stars.
%C Products of members of A007097.
%C A rooted star is a rooted tree whose branches are all rooted paths.
%e The sequence of rooted stars together with their Matula-Goebel numbers begins:
%e 1: o
%e 2: (o)
%e 3: ((o))
%e 4: (oo)
%e 5: (((o)))
%e 6: (o(o))
%e 8: (ooo)
%e 9: ((o)(o))
%e 10: (o((o)))
%e 11: ((((o))))
%e 12: (oo(o))
%e 15: ((o)((o)))
%e 16: (oooo)
%e 18: (o(o)(o))
%e 20: (oo((o)))
%e 22: (o(((o))))
%e 24: (ooo(o))
%e 25: (((o))((o)))
%e 27: ((o)(o)(o))
%e 30: (o(o)((o)))
%t rpQ[n_]:=n==1||PrimeQ[n]&&rpQ[PrimePi[n]];
%t Select[Range[100],And@@rpQ/@First/@FactorInteger[#]&]
%Y Cf. A007097, A056239, A061775, A109082, A109129, A112798, A196050, A324924, A325614, A325661, A325662.
%K nonn
%O 1,2
%A _Gus Wiseman_, May 13 2019
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