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a(n) = 1 if the arithmetic derivative of n is a multiple of 4, otherwise 0.
14

%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