%I #9 Apr 21 2022 17:23:59
%S 2,0,0,1,0,-2,0,-3,1,2,0,7,0,-2,-2,9,0,-1,0,-7,2,2,0,-25,1,-2,-3,7,0,
%T 4,0,-28,-2,2,-2,10,0,-2,2,25,0,-4,0,-7,7,2,0,91,1,-7,-2,7,0,1,2,-25,
%U 2,-2,0,-27,0,2,-7,90,-2,4,0,-7,-2,12,0,-60,0,-2,-1,7,-2,-4,0,-91,9,2,0,27,2,-2,2,25,0,-3,2
%N Sum of A353467 and its Dirichlet inverse.
%H Antti Karttunen, <a href="/A353469/b353469.txt">Table of n, a(n) for n = 1..10000</a>
%H Antti Karttunen, <a href="/A353469/a353469.txt">Data supplement: n, a(n) computed for n = 1..65537</a>
%H <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%F a(n) = A353467(n) + A353468(n) = A353467(n) + A353467(A252463(n)).
%F For n > 1, a(n) = -Sum_{d|n, 1<d<n} A353467(d) * A353468(n/d). [As the sequences are Dirichlet inverses of each other]
%F For all n >= 1, a(n) = a(A003961(n)) = a(A348717(n)).
%o (PARI)
%o A252463(n) = if(!(n%2),n/2,my(f=factor(n)); for(i=1, #f~, f[i,1] = precprime(f[i,1]-1)); factorback(f));
%o memoA353467 = Map();
%o A353467(n) = if(1==n,1,my(v); if(mapisdefined(memoA353467,n,&v), v, v = -sumdiv(n,d,if(d<n,A353467(A252463(n/d))*A353467(d),0)); mapput(memoA353467,n,v); (v)));
%o A353469(n) = (A353467(n)+A353467(A252463(n)));
%Y Cf. A003961, A252463, A348717, A353467, A353468.
%Y Cf. also A353459.
%K sign
%O 1,1
%A _Antti Karttunen_, Apr 21 2022