A359820 - OEIS

%I #13 Jan 14 2023 18:36:39

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

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

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

%N a(n) = 1 if n and n' are of different parity, otherwise 0. Here n' stands for the arithmetic derivative of n, A003415(n).

%H Antti Karttunen, <a href="/A359820/b359820.txt">Table of n, a(n) for n = 0..100000</a>

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

%F a(n) = A000035(A129283(n)).

%o (PARI)

%o A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));

%o A359820(n) = ((n+A003415(n))%2);

%Y Characteristic function of A359821, whose complement A359822 gives the positions of 0's.

%Y Parity of A129283 and of A168036.

%Y Cf. A000035, A003415, A359823 (Dirichlet inverse), A359824 (and its parity).

%Y Cf. also A347871.

%K nonn

%O 0

%A _Antti Karttunen_, Jan 14 2023