cp's OEIS Frontend

A258650 Tenth arithmetic derivative of n.

%I A258650 #11 Nov 03 2022 11:24:45
%S A258650 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 A258650 32624,0,1520,27,70464,0,0,0,235072,0,0,8592,47872,0,0,20096,24640,0,
%U A258650 0,0,65264,8592,0,0,130544,0,3424,8144,47872,0,57996,20096,198656,0,0
%N A258650 Tenth arithmetic derivative of n.
%H A258650 Alois P. Heinz, <a href="/A258650/b258650.txt">Table of n, a(n) for n = 0..10000</a>
%F A258650 a(n) = A003415^10(n).
%p A258650 d:= n-> n*add(i[2]/i[1], i=ifactors(n)[2]):
%p A258650 A:= proc(n, k) option remember; `if`(k=0, n, d(A(n, k-1))) end:
%p A258650 a:= n-> A(n, 10):
%p A258650 seq(a(n), n=0..70);
%o A258650 (Python)
%o A258650 from sympy import factorint
%o A258650 def A258650(n):
%o A258650     for _ in range(10):
%o A258650         if n <= 1: return 0
%o A258650         n = sum((n*e//p for p,e in factorint(n).items()))
%o A258650     return n # _Chai Wah Wu_, Nov 03 2022
%Y A258650 Column k=10 of A258651.
%Y A258650 Cf. A003415.
%K A258650 nonn
%O A258650 0,5
%A A258650 _Alois P. Heinz_, Jun 06 2015