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A258649 Ninth arithmetic derivative of n.

%I A258649 #11 Nov 03 2022 16:35:42
%S A258649 0,0,0,0,4,0,0,0,3424,0,0,0,8592,0,0,1520,20096,0,0,0,8144,0,0,0,
%T A258649 16304,0,752,27,20096,0,0,0,70464,0,0,3424,22288,0,0,8592,7744,0,0,0,
%U A258649 32624,3424,0,0,65264,0,1520,3120,22288,0,23112,8592,47872,0,0,0,47872
%N A258649 Ninth arithmetic derivative of n.
%H A258649 Alois P. Heinz, <a href="/A258649/b258649.txt">Table of n, a(n) for n = 0..10000</a>
%F A258649 a(n) = A003415^9(n).
%p A258649 d:= n-> n*add(i[2]/i[1], i=ifactors(n)[2]):
%p A258649 A:= proc(n, k) option remember; `if`(k=0, n, d(A(n, k-1))) end:
%p A258649 a:= n-> A(n, 9):
%p A258649 seq(a(n), n=0..70);
%o A258649 (Python)
%o A258649 from sympy import factorint
%o A258649 def A258649(n):
%o A258649     for _ in range(9):
%o A258649         if n <= 1: return 0
%o A258649         n = sum((n*e//p for p,e in factorint(n).items()))
%o A258649     return n # _Chai Wah Wu_, Nov 03 2022
%Y A258649 Column k=9 of A258651.
%Y A258649 Cf. A003415.
%K A258649 nonn
%O A258649 0,5
%A A258649 _Alois P. Heinz_, Jun 06 2015