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A354187 Sum of A348717 and its Dirichlet inverse.

%I A354187 #9 May 19 2022 16:43:01
%S A354187 2,0,0,4,0,8,0,8,4,8,0,16,0,8,8,16,0,16,0,32,8,8,0,24,4,8,8,48,0,40,0,
%T A354187 32,8,8,8,44,0,8,8,40,0,72,0,80,16,8,0,48,4,32,8,96,0,48,8,56,8,8,0,
%U A354187 56,0,8,32,64,8,120,0,128,8,72,0,64,0,8,16,144,8,168,0,80,16,8,0,72,8,8,8,88,0,80,8,176
%N A354187 Sum of A348717 and its Dirichlet inverse.
%C A354187 The first negative term is a(520) = -8.
%H A354187 Antti Karttunen, <a href="/A354187/b354187.txt">Table of n, a(n) for n = 1..20000</a>
%H A354187 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%F A354187 a(n) = A348717(n) + A354186(n).
%F A354187 a(1) = 2, and for n > 1, a(n) = -Sum_{d|n, 1<d<n} A348717(d) * A354186(n/d).
%o A354187 (PARI)
%o A354187 A348717(n) = if(1==n, 1, my(f = factor(n), k = primepi(f[1, 1])-1); for (i=1, #f~, f[i, 1] = prime(primepi(f[i, 1])-k)); factorback(f));
%o A354187 memoA354186 = Map();
%o A354187 A354186(n) = if(1==n,1,my(v); if(mapisdefined(memoA354186,n,&v), v, v = -sumdiv(n,d,if(d<n,A348717(n/d)*A354186(d),0)); mapput(memoA354186,n,v); (v)));
%o A354187 A354187(n) = (A348717(n)+A354186(n));
%Y A354187 Cf. A348717, A354186.
%K A354187 sign
%O A354187 1,1
%A A354187 _Antti Karttunen_, May 19 2022