A258650 - OEIS

%I #11 Nov 03 2022 11:24:45

%S 0,0,0,0,4,0,0,0,8592,0,0,0,20096,0,0,3424,70464,0,0,0,16304,0,0,0,

%T 32624,0,1520,27,70464,0,0,0,235072,0,0,8592,47872,0,0,20096,24640,0,

%U 0,0,65264,8592,0,0,130544,0,3424,8144,47872,0,57996,20096,198656,0,0

%N Tenth arithmetic derivative of n.

%H Alois P. Heinz, <a href="/A258650/b258650.txt">Table of n, a(n) for n = 0..10000</a>

%F a(n) = A003415^10(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, 10):

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

%o (Python)

%o from sympy import factorint

%o def A258650(n):

%o     for _ in range(10):

%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=10 of A258651.

%Y Cf. A003415.

%K nonn

%O 0,5

%A _Alois P. Heinz_, Jun 06 2015