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A379967 Arithmetic derivative of {n divided by its largest squarefree divisor}: a(n) = A003415(A003557(n)).

%I A379967 #7 Jan 22 2025 08:51:54
%S A379967 0,0,0,1,0,0,0,4,1,0,0,1,0,0,0,12,0,1,0,1,0,0,0,4,1,0,6,1,0,0,0,32,0,
%T A379967 0,0,5,0,0,0,4,0,0,0,1,1,0,0,12,1,1,0,1,0,6,0,4,0,0,0,1,0,0,1,80,0,0,
%U A379967 0,1,0,0,0,16,0,0,1,1,0,0,0,12,27,0,0,1,0,0,0,4,0,1,0,1,0,0,0,32,0,1,1,7,0,0,0,4
%N A379967 Arithmetic derivative of {n divided by its largest squarefree divisor}: a(n) = A003415(A003557(n)).
%H A379967 Antti Karttunen, <a href="/A379967/b379967.txt">Table of n, a(n) for n = 1..65537</a>
%F A379967 a(n) = A003415(A003557(n)).
%o A379967 (PARI)
%o A379967 A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
%o A379967 A003557(n) = (n/factorback(factor(n)[, 1]));
%o A379967 A379967(n) = A003415(A003557(n));
%Y A379967 Cf. A003415, A003557.
%Y A379967 Cf. also A028235, A341998, A342001.
%K A379967 nonn
%O A379967 1,8
%A A379967 _Antti Karttunen_, Jan 22 2025