%I #14 Apr 23 2022 18:13:01
%S 1,1,0,0,1,0,0,0,1,0,0,0,1,0,0,1,1,0,0,0,1,0,0,0,1,0,0,0,1,0,0,0,1,0,
%T 0,1,1,0,0,1,1,0,0,0,1,0,0,0,1,0,0,1,1,0,0,1,1,0,0,0,1,0,0,0,1,0,0,0,
%U 1,0,0,0,1,0,0,0,1,0,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0,0,0,1,0
%N a(n) = 1 if the arithmetic derivative of n is a multiple of 4, otherwise 0.
%H Antti Karttunen, <a href="/A353494/b353494.txt">Table of n, a(n) for n = 0..65537</a>
%H <a href="/index/Ch#char_fns">Index entries for characteristic functions</a>
%F a(n) = 1 if A353493(n) = 0, otherwise a(n) = 0.
%F For all n > 1, a(n) <= A341996(n) <= A341999(n). [This means that a membership in A327864 implies also a membership in A327929 and in A099309]
%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 A353494(n) = (0==(A003415(n)%4));
%Y Characteristic function of A327864.
%Y Cf. A003415, A353493, A353495, and also A165560, A341996, A341999.
%K nonn
%O 0
%A _Antti Karttunen_, Apr 23 2022