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A053471 a(n) is the cototient of n (A051953) iterated 3 times.

%I A053471 #15 May 31 2018 02:09:09
%S A053471 0,0,0,0,0,1,0,1,0,2,0,2,0,2,0,2,0,4,0,4,1,4,0,4,0,4,1,4,0,8,0,4,0,8,
%T A053471 0,8,0,8,1,8,0,12,0,8,3,8,0,8,0,12,0,8,0,16,1,8,3,12,0,16,0,8,3,8,0,
%U A053471 16,0,16,1,16,0,16,0,12,1,16,0,24,0,16,3,22,0,24,3,16,0,16,0,24,0,16,1,16,0
%N A053471 a(n) is the cototient of n (A051953) iterated 3 times.
%C A053471 Iteration of A051953 behaves similarly to that of Euler Phi. Analogous 3rd iterates for A000005 or A000010 are A036455 and A049099.
%C A053471 It is assumed here that the value of A051953 at 0 is 0. - _Antti Karttunen_, Dec 22 2017
%H A053471 Antti Karttunen, <a href="/A053471/b053471.txt">Table of n, a(n) for n = 1..16384</a>
%e A053471 n=50, n_1 = n - phi(n) = 50 - 20 = 30, n_2 = n_1 - Phi(n_1) = 30 - 8 = 22, n_3 = 22 - Phi(22) = 12 so the 50th term is 12.
%t A053471 Array[Nest[# - EulerPhi@ # &, #, 3] &, 95] (* _Michael De Vlieger_, Dec 23 2017 *)
%o A053471 (PARI)
%o A053471 A051953(n) = if(!n,n,(n-eulerphi(n))); \\ With modification that returns zero for zero.
%o A053471 A053471(n) = A051953(A051953(A051953(n))); \\ _Antti Karttunen_, Dec 22 2017
%Y A053471 Cf. A051953, A000005, A000010, A036455, A049099.
%Y A053471 Cf. A053470, A053472, A053473.
%K A053471 nonn
%O A053471 1,10
%A A053471 _Labos Elemer_, Jan 14 2000