%I #12 Dec 01 2022 08:56:36
%S 0,0,0,1,0,0,0,0,1,1,0,0,0,1,0,0,0,0,0,0,0,0,0,1,1,0,0,0,0,0,0,0,1,1,
%T 1,0,0,1,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,0,1,0,1,0,0,0,1,0,0,0,0,
%U 1,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0,0,0,0,0,0,0,0,1,0
%N a(n) = 1 if A349905(n) == 2 (mod 4), otherwise 0. Here A349905(n) is the arithmetic derivative applied to the prime shifted n.
%H Antti Karttunen, <a href="/A358752/b358752.txt">Table of n, a(n) for n = 1..100000</a>
%H <a href="/index/Ch#char_fns">Index entries for characteristic functions</a>
%H <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%F a(n) = 1-A152822(A349905(n)).
%F a(n) = A353495(A003961(n)).
%F a(n) = A065043(n) - A358750(n).
%F a(n) = [3-A010873(A001222(n)) == A010873(A003961(n))], where [ ] is the Iverson bracket.
%F a(n) = [bigomega(n) == 2*A246260(n) (mod 4)].
%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 A003961(n) = { my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
%o A349905(n) = A003415(A003961(n));
%o A358752(n) = (2==(A349905(n)%4));
%o (PARI)
%o A010873(n) = (n%4);
%o A358752(n) = (3-A010873(bigomega(n))==A010873(A003961(n)));
%Y Characteristic function of A358762.
%Y Cf. A001222, A003415, A003961, A010873, A065043, A152822, A246260, A349905, A353495, A358750.
%K nonn
%O 1
%A _Antti Karttunen_, Nov 29 2022