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A228731 Number of independent subsets in the rooted tree with Matula-Goebel number n that contain the root.

%I A228731 #19 Sep 20 2019 10:32:03
%S A228731 1,1,2,1,3,2,4,1,4,3,5,2,6,4,6,1,5,4,8,3,8,5,9,2,9,6,8,4,10,6,8,1,10,
%T A228731 5,12,4,12,8,12,3,8,8,10,5,12,9,15,2,16,9,10,6,16,8,15,4,16,10,9,6,18,
%U A228731 8,16,1,18,10,9,5,18,12,20,4,15,12,18,8,20,12
%N A228731 Number of independent subsets in the rooted tree with Matula-Goebel number n that contain the root.
%C A228731 A184165(n) = a(n) + A228732(n);
%C A228731 this sequence and A228732 are defined by a pair of mutually recursive functions, see A184165 for definition (called b and c there).
%H A228731 Reinhard Zumkeller, <a href="/A228731/b228731.txt">Table of n, a(n) for n = 1..10000</a>
%H A228731 <a href="/index/Mat#matula">Index entries for sequences related to Matula-Goebel numbers</a>
%F A228731 Completely multiplicative with a(prime(t)) = A228732(t). - _Andrew Howroyd_, Aug 01 2018
%t A228731 r[n_] := FactorInteger[n][[1, 1]];
%t A228731 s[n_] := n/r[n];
%t A228731 A[n_] := A[n] = If[n==1, {1, 1}, If[PrimeOmega[n]==1, {A[PrimePi[n]][[2]], A[PrimePi[n]] // Total}, A[r[n]] * A[s[n]]]];
%t A228731 a[n_] := A[n][[1]];
%t A228731 a /@ Range[1, 80] (* _Jean-François Alcover_, Sep 20 2019 *)
%o A228731 (Haskell) see A184165.
%Y A228731 Cf. A184165, A228732.
%K A228731 nonn,mult
%O A228731 1,3
%A A228731 _Emeric Deutsch_ and _Reinhard Zumkeller_, Sep 01 2013