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%I #4 Jun 12 2015 20:44:17
%S 0,0,0,0,4,0,4,4,80,80,2,1,208,4,12,20,512,4,20,32,512,53,30,32,324,
%T 32,16,864,704,3,80,2,2304,32,3,7,460,80,6,704,460,4,25,8,2432,228,7,
%U 12,6720,332,20,56,1188,208,3888,116,424,32,156,4,956,12,80,764
%N Fourth pi-based arithmetic derivative of n.
%H Alois P. Heinz, <a href="/A258854/b258854.txt">Table of n, a(n) for n = 0..10000</a>
%F a(n) = A258851^4(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, 4):
%p seq(a(n), n=0..100);
%Y Column k=4 of A258850.
%Y Cf. A000720, A258851.
%K nonn
%O 0,5
%A _Alois P. Heinz_, Jun 12 2015