%I #7 Jun 25 2015 08:03:34

%S 0,0,0,1,4,2,4,4,20,20,5,3,32,7,19,8,80,4,37,12,80,25,26,12,76,53,30,

%T 135,64,11,16,5,208,12,11,13,188,20,41,64,188,6,21,15,192,88,13,19,

%U 448,116,86,58,108,32,351,49,156,53,56,7,260,33,16,332,704,73

%N Second pi-based arithmetic derivative of n.

%H Alois P. Heinz, <a href="/A258852/b258852.txt">Table of n, a(n) for n = 0..10000</a>

%F a(n) = A258851^2(n).

%F a(A258862(n)) = n.

%p with(numtheory):

%p d:= n-> n*add(i[2]*pi(i[1])/i[1], i=ifactors(n)[2]):

%p A:= proc(n, k) option remember; `if`(k=0, n, d(A(n, k-1))) end:

%p a:= n-> A(n, 2):

%p seq(a(n), n=0..100);

%Y Column k=2 of A258850.

%Y Cf. A000720, A258851, A258862.

%K nonn

%O 0,5

%A _Alois P. Heinz_, Jun 12 2015