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%I #22 Nov 03 2022 11:24:11
%S 0,0,0,0,4,0,0,0,1520,0,0,0,235072,0,0,705280,278539264,0,0,0,
%T 226593936,0,0,0,295266178368,0,24143851798528,27,
%U 10557680820452065280,0,0,0,2821525007683005301391360,0,0,2821525007683005301391360,43942858408664114852524638339072
%N n-th arithmetic derivative of n.
%C a(n) is zero for all prime n.
%H Alois P. Heinz, <a href="/A185232/b185232.txt">Table of n, a(n) for n = 0..80</a>
%t dn[0]=0; dn[1]=0; dn[n_] := Module[{f=Transpose[FactorInteger[n]]}, If[PrimeQ[n], 1, Plus@@(n*f[[2]]/f[[1]])]]; Table[Nest[dn,n,n], {n,50}]
%o (Python)
%o from sympy import factorint
%o def A185232(n):
%o for _ in range(n):
%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 Cf. A003415.
%Y Main diagonal of A258651.
%K nonn
%O 0,5
%A _José María Grau Ribas_, Jan 24 2012
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