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%I #15 Oct 15 2013 22:31:08
%S 0,-1,0,0,1,-1,3,0,2,0,5,-2,7,0,-2,0,7,0,11,0,2,2,11,-4,8,2,6,0,15,-6,
%T 21,0,0,2,6,0,23,4,8,0,23,0,29,4,4,4,23,-8,24,4,-2,4,27,0,16,0,12,8,
%U 29,-12,43,6,6,0,16,-10,45,4,4,-6,45,0,47,6,0,8,28,-2,53,0,18,12,41,0,20,10,2,8,47,-4,30,8,24,8,26,-16,63,6,20,8,59,-8
%N Cototient(totient(n)) - totient(cototient(n)).
%H Harry J. Smith, <a href="/A065152/b065152.txt">Table of n, a(n) for n=1,...,1000</a>
%F a(n) = (phi(n) - phi(phi(n))) - (phi(n - phi(n))) = A000010(A051953(n)) - A051953(A000010(n)).
%e a(100) = 8, since phi(100) = 40, 100 - phi(100) = 60 = cototient(100), cototient(40) = 40 - 16 = 24, totient(60) = 16 so a(100) = 24 - 16 = 8.
%t coTotient[n_] := n - EulerPhi@n; A065152[n_] := coTotient@ EulerPhi@ n - EulerPhi@ coTotient@ n; Array[A065152, 102] (* _Robert G. Wilson v_, Feb 24 2010 *)
%o (PARI) { for (n = 1, 1000, t=eulerphi(n); c=n - t; if (n>1, a=t - eulerphi(t) - eulerphi(c), a=0); write("b065152.txt", n, " ", a) ) } \\ _Harry J. Smith_, Oct 13 2009
%Y Cf. A065153, A065154, A065155 (positions of zeros, negative, and positive numbers).
%K sign
%O 1,7
%A _Labos Elemer_, Oct 19 2001
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