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Tenth pi-based arithmetic derivative of n.
2

%I #4 Jun 12 2015 20:47:53

%S 0,0,0,0,4,0,4,4,622592,622592,0,0,4931584,4,2304,12288,38944768,4,

%T 12288,81920,38944768,2304,512,81920,714096,81920,12288,65719296,

%U 2298880,0,622592,0,278380544,81920,0,4,85988,622592,4,2298880,85988,4,208,512,13319168

%N Tenth pi-based arithmetic derivative of n.

%H Alois P. Heinz, <a href="/A258860/b258860.txt">Table of n, a(n) for n = 0..10000</a>

%F a(n) = A258851^10(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, 10):

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

%Y Column k=10 of A258850.

%Y Cf. A000720, A258851.

%K nonn

%O 0,5

%A _Alois P. Heinz_, Jun 12 2015