A359815 - OEIS

%I #10 Jan 16 2023 16:12:19

%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,

%T 0,-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,

%U 0,-1,0,0,0,8,-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 A359770, where A359770(n) = 1 if n and bigomega(n) are of different parity, otherwise 0.

%H Antti Karttunen, <a href="/A359815/b359815.txt">Table of n, a(n) for n = 1..65537</a>

%F a(1) = 1, and for n > 1, a(n) = -Sum_{d|n, d<n} A359770(n/d) * a(d).

%o (PARI)

%o A359770(n) = ((n-bigomega(n))%2);

%o memoA359815 = Map();

%o A359815(n) = if(1==n,1,my(v); if(mapisdefined(memoA359815,n,&v), v, v = -sumdiv(n,d,if(d<n,A359770(n/d)*A359815(d),0)); mapput(memoA359815,n,v); (v)));

%Y Cf. A001222, A069345, A353556, A353557, A359770, A359816 (parity of terms), A359817 (positions of odd terms).

%Y Cf. also A358777 (Dirichlet inverse of A353557), A359763 [= a(A003961(n))], A359814.

%K sign

%O 1,8

%A _Antti Karttunen_, Jan 15 2023