cp's OEIS Frontend

A303024 Matula-Goebel numbers of anti-binary (no binary branchings) rooted trees.

%I A303024 #10 Aug 16 2018 08:51:18
%S A303024 1,2,3,5,8,11,12,16,18,19,20,24,27,30,31,32,36,37,40,44,45,48,50,53,
%T A303024 54,60,61,64,66,67,71,72,75,76,80,81,88,89,90,96,99,100,103,108,110,
%U A303024 113,114,120,124,125,127,128,131,132,135,144,148,150,151,152,157
%N A303024 Matula-Goebel numbers of anti-binary (no binary branchings) rooted trees.
%e A303024 The sequence of anti-binary rooted trees together with their Matula-Goebel numbers begins:
%e A303024    1: o
%e A303024    2: (o)
%e A303024    3: ((o))
%e A303024    5: (((o)))
%e A303024    8: (ooo)
%e A303024   11: ((((o))))
%e A303024   12: (oo(o))
%e A303024   16: (oooo)
%e A303024   18: (o(o)(o))
%e A303024   19: ((ooo))
%e A303024   20: (oo((o)))
%e A303024   24: (ooo(o))
%e A303024   27: ((o)(o)(o))
%e A303024   30: (o(o)((o)))
%e A303024   31: (((((o)))))
%t A303024 abQ[n_]:=Or[n==1,And[PrimeOmega[n]!=2,And@@Cases[FactorInteger[n],{p_,_}:>abQ[PrimePi[p]]]]]
%t A303024 Select[Range[100],abQ]
%Y A303024 Cf. A000081, A000598, A001190, A001678, A007097, A061775, A111299, A292050, A298422, A298424.
%Y A303024 Cf. A303022, A303023, A303025, A303026, A303027.
%K A303024 nonn
%O A303024 1,2
%A A303024 _Gus Wiseman_, Aug 15 2018