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A353496 The arithmetic derivative of the largest proper divisor of n, reduced modulo 4, with a(1) = 0.

%I A353496 #7 Apr 27 2022 13:55:07
%S A353496 0,0,0,1,0,1,0,0,1,1,0,1,0,1,1,0,0,2,0,3,1,1,0,0,1,1,2,1,0,0,0,0,1,1,
%T A353496 1,1,0,1,1,0,0,2,0,1,0,1,0,0,1,2,1,3,0,3,1,0,1,1,0,3,0,1,2,0,1,2,0,3,
%U A353496 1,0,0,0,0,1,2,1,1,0,0,0,3,1,0,1,1,1,1,0,0,3,1,1,1,1,1,0,0,2,2,1,0,0,0,0,0
%N A353496 The arithmetic derivative of the largest proper divisor of n, reduced modulo 4, with a(1) = 0.
%H A353496 Antti Karttunen, <a href="/A353496/b353496.txt">Table of n, a(n) for n = 1..65537</a>
%F A353496 a(n) = A353493(A032742(n)) = A010873(A003415(A032742(n))).
%o A353496 (PARI)
%o A353496 A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
%o A353496 A032742(n) = if(1==n,n,n/vecmin(factor(n)[,1]));
%o A353496 A353496(n) = (A003415(A032742(n))%4);
%Y A353496 Cf. A003415, A010873, A032742, A353493.
%Y A353496 Cf. also A353490.
%K A353496 nonn
%O A353496 1,18
%A A353496 _Antti Karttunen_, Apr 26 2022