A359764 - OEIS

%I #15 Jan 14 2023 17:47:18

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

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

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

%N Parity of A359763, where A359763 is the Dirichlet inverse of characteristic function of the numbers with an even number of prime factors (counted with multiplicity).

%H Antti Karttunen, <a href="/A359764/b359764.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) = A359763(n) mod 2.

%F a(n) = A359774(A003961(n)) = A359781(A003961(n)) = A359824(A003961(n)).

%F a(n) <= A065043(n). [See comments in A359763]

%F a(A030229(n)) = 1 for all n.

%o (PARI) A359764(n) = (A359763(n)%2);

%Y Parity of A359763 and of A359791.

%Y Characteristic function of A359765, whose complement A359766 gives the positions of 0's.

%Y Cf. A003961, A030229, A359763, A359767 (where differs from A065043).

%Y Cf. also A359595, A359774, A359781, A359824 for similar constructions.

%K nonn

%O 1

%A _Antti Karttunen_, Jan 13 2023