A258853 - OEIS

%I #9 Aug 31 2015 21:08:23

%S 0,0,0,0,4,1,4,4,32,32,3,2,80,4,8,12,208,4,12,20,208,30,25,20,108,16,

%T 53,351,192,5,32,3,512,20,5,6,248,32,13,192,248,7,26,19,704,172,6,8,

%U 1600,156,71,49,324,80,864,56,332,16,116,4,536,37,32,424,2432

%N Third pi-based arithmetic derivative of n.

%H Alois P. Heinz, <a href="/A258853/b258853.txt">Table of n, a(n) for n = 0..10000</a>

%F a(n) = A258851^3(n).

%F a(A258995(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, 3):

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

%Y Column k=3 of A258850.

%Y Cf. A000720, A258851, A258995.

%K nonn,look

%O 0,5

%A _Alois P. Heinz_, Jun 12 2015