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%I #5 Jun 12 2015 20:41:51
%S 0,0,0,0,4,0,4,4,12288,81920,0,0,278380544,4,4931584,278380544,
%T 14768867966976,4,128412352512,14768867966976,375877192068366336,
%U 14768867966976,14768867966976,375877192068366336
%N The n-th pi-based arithmetic derivative of n.
%F a(n) = A258851^n(n) = A258850(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..23);
%Y Main diagonal of A258850.
%Y Cf. A000720, A258851.
%K nonn
%O 0,5
%A _Alois P. Heinz_, Jun 12 2015