A258649 - OEIS

%I #11 Nov 03 2022 16:35:42

%S 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 16304,0,752,27,20096,0,0,0,70464,0,0,3424,22288,0,0,8592,7744,0,0,0,

%U 32624,3424,0,0,65264,0,1520,3120,22288,0,23112,8592,47872,0,0,0,47872

%N Ninth arithmetic derivative of n.

%H Alois P. Heinz, <a href="/A258649/b258649.txt">Table of n, a(n) for n = 0..10000</a>

%F a(n) = A003415^9(n).

%p d:= n-> n*add(i[2]/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, 9):

%p seq(a(n), n=0..70);

%o (Python)

%o from sympy import factorint

%o def A258649(n):

%o     for _ in range(9):

%o         if n <= 1: return 0

%o         n = sum((n*e//p for p,e in factorint(n).items()))

%o     return n # _Chai Wah Wu_, Nov 03 2022

%Y Column k=9 of A258651.

%Y Cf. A003415.

%K nonn

%O 0,5

%A _Alois P. Heinz_, Jun 06 2015