A353496 - OEIS

%I #7 Apr 27 2022 13:55:07

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

%H Antti Karttunen, <a href="/A353496/b353496.txt">Table of n, a(n) for n = 1..65537</a>

%F a(n) = A353493(A032742(n)) = A010873(A003415(A032742(n))).

%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 A032742(n) = if(1==n,n,n/vecmin(factor(n)[,1]));

%o A353496(n) = (A003415(A032742(n))%4);

%Y Cf. A003415, A010873, A032742, A353493.

%Y Cf. also A353490.

%K nonn

%O 1,18

%A _Antti Karttunen_, Apr 26 2022