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A229340 Euler totient function of the arithmetic derivative of n: a(n) = phi(n'), a(1) = 0.

%I A229340 #50 Feb 25 2018 09:52:15
%S A229340 0,1,1,2,1,4,1,4,2,6,1,8,1,6,4,16,1,12,1,8,4,12,1,20,4,8,18,16,1,30,1,
%T A229340 32,6,18,4,16,1,12,8,32,1,40,1,16,24,20,1,48,6,24,8,24,1,54,8,44,10,
%U A229340 30,1,44,1,20,32,64,6,60,1,24,12,58,1,48,1,24,40,32,6,70,1,80,36,42,1,60,10,24,16,48,1,80,8,32,16,42,8
%N A229340 Euler totient function of the arithmetic derivative of n: a(n) = phi(n'), a(1) = 0.
%C A229340 a(1) = 0 by convention. - _Antti Karttunen_, Oct 30 2017
%H A229340 Antti Karttunen, <a href="/A229340/b229340.txt">Table of n, a(n) for n = 1..16384</a>
%F A229340 a(1) = 0; and for n > 1, a(n) = A000010(A003415(n)).
%e A229340 For n=4 phi(n')=phi(4')=phi(4)=2.
%e A229340 For n=7 phi(n')=phi(7')=phi(1)=1.
%t A229340 Array[EulerPhi@ If[Abs@ # < 2, 0, # Total[#2/#1 & @@@ FactorInteger[Abs@ #]]] &, 75] (* _Michael De Vlieger_, Oct 30 2017, after _Michael Somos_ at A003415 *)
%o A229340 (PARI) rd(n) = {local(fac); if(n<1, 0, fac=factor(n); sum(i=1, matsize(fac)[1], n*fac[i, 2]/fac[i, 1];));}
%o A229340 a(n) = eulerphi(rd(n)); \\ _Michel Marcus_, Sep 24 2013
%Y A229340 Cf. A000010, A003415.
%K A229340 nonn
%O A229340 1,4
%A A229340 _Luca Brigada Villa_, Sep 24 2013
%E A229340 Description/formula clarified and more terms added by _Antti Karttunen_, Oct 30 2017