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Dirichlet inverse of A359769, where A359769(n) = A353557(n) - A353556(n).
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%I #10 Jan 16 2023 16:11:59

%S 1,1,0,1,0,0,0,2,-1,0,0,1,0,0,-1,3,0,-1,0,1,-1,0,0,2,-1,0,0,1,0,-1,0,

%T 5,-1,0,-1,-1,0,0,-1,2,0,-1,0,1,0,0,0,4,-1,-1,-1,1,0,0,-1,2,-1,0,0,-1,

%U 0,0,0,8,-1,-1,0,1,-1,-1,0,-2,0,0,0,1,-1,-1,0,4,0,0,0,-1,-1,0,-1,2,0,0,-1,1,-1,0,-1,8

%N Dirichlet inverse of A359769, where A359769(n) = A353557(n) - A353556(n).

%H Antti Karttunen, <a href="/A359814/b359814.txt">Table of n, a(n) for n = 1..16384</a>

%F a(1) = 1, and for n > 1, a(n) = -Sum_{d|n, d<n} A359769(n/d) * a(d).

%o (PARI)

%o A353556(n) = ((!(n%2))&&(bigomega(n)%2));

%o A353557(n) = ((n%2)&&(!(bigomega(n)%2)));

%o A359769(n) = (A353557(n)-A353556(n));

%o memoA359814 = Map();

%o A359814(n) = if(1==n,1,my(v); if(mapisdefined(memoA359814,n,&v), v, v = -sumdiv(n,d,if(d<n,A359769(n/d)*A359814(d),0)); mapput(memoA359814,n,v); (v)));

%Y Cf. A001222, A353556, A353557, A359769, A359816 (parity of terms).

%Y Cf. also A358777 (Dirichlet inverse of A353557), A359763 [= a(A003961(n))], A359815.

%K sign

%O 1,8

%A _Antti Karttunen_, Jan 15 2023