%I #11 Jan 16 2023 15:44:11

%S 1,1,0,1,0,0,0,0,1,0,0,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0,1,0,1,1,0,

%T 1,1,0,0,1,0,0,1,0,1,0,0,0,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0,0,1,1,0,1,

%U 1,1,0,0,0,0,0,1,1,1,0,0,0,0,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0,0,0,1,0,1,1,0,0,1,1,1,0,0,1,0,1

%N Parity of A359815, where A359815 is the Dirichlet inverse of A359770, which is the characteristic function for numbers k such that k and bigomega(k) are of different parity.

%C Note that here a(n) = 1 does not imply that A359770(n) = 1 also. The difference A359770(n) - a(n) can be -1, 0, or +1. This in contrast to sequences like A359764, A359774 and A359781.

%H Antti Karttunen, <a href="/A359816/b359816.txt">Table of n, a(n) for n = 1..100000</a>

%H <a href="/index/Ch#char_fns">Index entries for characteristic functions</a>

%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)));

%o A359816(n) = (A359815(n)%2);

%Y Parity of A359814 and A359815.

%Y Characteristic function of A359817.

%Y Cf. A001222, A353556, A353557, A359770.

%Y Cf. also A359764 [= a(A003961(n))], A359774, A359781.

%K nonn

%O 1

%A _Antti Karttunen_, Jan 15 2023