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%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