%I #11 Mar 14 2021 20:42:17

%S 0,1,1,0,1,5,1,4,6,7,1,4,1,9,8,0,1,3,1,4,10,13,1,20,10,15,0,4,1,1,1,

%T 16,14,19,12,24,1,21,16,28,1,41,1,4,39,25,1,16,14,45,20,4,1,27,16,36,

%U 22,31,1,32,1,33,51,0,18,61,1,4,26,59,1,12,1,39,55,4,18,71,1,16,27,43,1,40,22,45,32,52,1,33

%N Arithmetic derivative of n, taken modulo n: a(n) = A003415(n) mod n.

%H Antti Karttunen, <a href="/A342014/b342014.txt">Table of n, a(n) for n = 1..16384</a>

%H Antti Karttunen, <a href="/A342014/a342014.txt">Data supplement: n, a(n) computed for n = 1..65537</a>

%F a(n) = A003415(n) mod 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 A342014(n) = (A003415(n)%n);

%Y Cf. A003415, A072873 (positions of zeros), A085731 [= gcd(n, a(n))], A342015 [= A342014(A276086(n))].

%K nonn

%O 1,6

%A _Antti Karttunen_, Mar 04 2021