%I #7 Feb 06 2024 16:24:26

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

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

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

%N a(n) = 1 if n > 1 and A276085(A003415(n)) == n (mod 4), otherwise 0, where A003415 is the arithmetic derivative, and A276085 is the primorial base log-function.

%H Antti Karttunen, <a href="/A369665/b369665.txt">Table of n, a(n) for n = 0..100000</a>

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

%o (PARI)

%o A002110(n) = prod(i=1,n,prime(i));

%o A276085(n) = { my(f = factor(n)); sum(k=1, #f~, f[k, 2]*A002110(primepi(f[k, 1])-1)); };

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

%o A369665(n) = ((n>1) && ((A276085(A003415(n))%4)==(n%4)));

%Y Characteristic function of A369666.

%Y Cf. A003415, A276085.

%K nonn

%O 0

%A _Antti Karttunen_, Feb 06 2024