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A228732 Number of independent subsets in the rooted tree with Matula-Goebel number n that do not contain the root.

%I A228732 #16 Sep 20 2019 10:32:11
%S A228732 1,2,3,4,5,6,5,8,9,10,8,12,8,10,15,16,9,18,9,20,15,16,13,24,25,16,27,
%T A228732 20,13,30,13,32,24,18,25,36,14,18,24,40,14,30,14,32,45,26,21,48,25,50,
%U A228732 27,32,17,54,40,40,27,26,14,60,22,26,45,64,40,48,17,36
%N A228732 Number of independent subsets in the rooted tree with Matula-Goebel number n that do not contain the root.
%C A228732 A184165(n) = A228731(n) + a(n);
%C A228732 this sequence and A228731 are defined by a pair of mutually recursive functions, see A184165 for definition (called b and c there).
%H A228732 Reinhard Zumkeller, <a href="/A228732/b228732.txt">Table of n, a(n) for n = 1..10000</a>
%H A228732 <a href="/index/Mat#matula">Index entries for sequences related to Matula-Goebel numbers</a>
%F A228732 Completely multiplicative with a(prime(t)) = A228731(t) + A228732(t). - _Andrew Howroyd_, Aug 01 2018
%t A228732 r[n_] := FactorInteger[n][[1, 1]];
%t A228732 s[n_] := n/r[n];
%t A228732 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 A228732 a[n_] := A[n][[2]];
%t A228732 a /@ Range[1, 80] (* _Jean-François Alcover_, Sep 20 2019 *)
%o A228732 (Haskell) see A184165.
%Y A228732 Cf. A184165, A228731.
%K A228732 nonn,mult
%O A228732 1,2
%A A228732 _Emeric Deutsch_ and _Reinhard Zumkeller_, Sep 01 2013