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a(n) = 1 if n and bigomega(n) are of different parity, otherwise 0. Here bigomega (A001222) gives the number of prime factors of n with multiplicity.
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%I #12 Jan 16 2023 15:44:35

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

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

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

%N a(n) = 1 if n and bigomega(n) are of different parity, otherwise 0. Here bigomega (A001222) gives the number of prime factors of n with multiplicity.

%H Antti Karttunen, <a href="/A359770/b359770.txt">Table of n, a(n) for n = 1..100000</a>

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

%F a(n) = A000035(A069345(n)) = A000035(n-A001222(n)).

%F a(n) = A353556(n) + A353557(n).

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

%Y Parity of A069345, and of A359769 (also the absolute values).

%Y Characteristic function of A359771, whose complement A359772 gives the positions of 0's.

%Y Sum of A353556 and A353557.

%Y Cf. A000035, A001222, A065043 [= a(A003961(n))], A359815 (Dirichlet inverse).

%K nonn

%O 1

%A _Antti Karttunen_, Jan 15 2023