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A298479 Matula-Goebel numbers of rooted trees in which all positive outdegrees are different.

%I A298479 #6 Jan 22 2018 03:07:19
%S A298479 1,2,4,6,7,8,12,16,19,24,28,32,38,42,48,52,53,56,57,64,68,74,84,96,
%T A298479 104,106,107,112,128,131,134,136,152,159,163,168,178,192,208,212,224,
%U A298479 228,256,262,263,272,296,304,311,318,336,356,384,393,416,446,448,456
%N A298479 Matula-Goebel numbers of rooted trees in which all positive outdegrees are different.
%e A298479 Sequence of trees begins:
%e A298479 1  o
%e A298479 2  (o)
%e A298479 4  (oo)
%e A298479 6  (o(o))
%e A298479 7  ((oo))
%e A298479 8  (ooo)
%e A298479 12 (oo(o))
%e A298479 16 (oooo)
%e A298479 19 ((ooo))
%e A298479 24 (ooo(o))
%e A298479 28 (oo(oo))
%e A298479 32 (ooooo)
%e A298479 38 (o(ooo))
%e A298479 42 (o(o)(oo))
%e A298479 48 (oooo(o))
%e A298479 52 (oo(o(o)))
%e A298479 53 ((oooo))
%e A298479 56 (ooo(oo))
%e A298479 57 ((o)(ooo))
%e A298479 64 (oooooo)
%e A298479 68 (oo((oo)))
%e A298479 74 (o(oo(o)))
%e A298479 84 (oo(o)(oo))
%e A298479 96 (ooooo(o))
%t A298479 MGtree[n_]:=If[n===1,{},MGtree/@Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A298479 doQ[n_]:=Or[n===1,UnsameQ@@Length/@Cases[MGtree[n],{__},{0,Infinity}]];
%t A298479 Select[Range[1000],doQ]
%Y A298479 Cf. A000081, A001221, A004111, A007097, A032305, A061775, A111299, A276625, A290760, A297571, A298120, A298422, A298424, A298478.
%K A298479 nonn
%O A298479 1,2
%A A298479 _Gus Wiseman_, Jan 19 2018