A229340 - OEIS

%I #50 Feb 25 2018 09:52:15

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

%C a(1) = 0 by convention. - _Antti Karttunen_, Oct 30 2017

%H Antti Karttunen, <a href="/A229340/b229340.txt">Table of n, a(n) for n = 1..16384</a>

%F a(1) = 0; and for n > 1, a(n) = A000010(A003415(n)).

%e For n=4 phi(n')=phi(4')=phi(4)=2.

%e For n=7 phi(n')=phi(7')=phi(1)=1.

%t Array[EulerPhi@ If[Abs@ # < 2, 0, # Total[#2/#1 & @@@ FactorInteger[Abs@ #]]] &, 75] (* _Michael De Vlieger_, Oct 30 2017, after _Michael Somos_ at A003415 *)

%o (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 a(n) = eulerphi(rd(n)); \\ _Michel Marcus_, Sep 24 2013

%Y Cf. A000010, A003415.

%K nonn

%O 1,4

%A _Luca Brigada Villa_, Sep 24 2013

%E Description/formula clarified and more terms added by _Antti Karttunen_, Oct 30 2017