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%I #16 May 31 2018 02:10:45
%S 0,0,0,0,0,0,0,0,0,1,0,1,0,1,0,1,0,2,0,2,0,2,0,2,0,2,0,2,0,4,0,2,0,4,
%T 0,4,0,4,0,4,0,8,0,4,1,4,0,4,0,8,0,4,0,8,0,4,1,8,0,8,0,4,1,4,0,8,0,8,
%U 0,8,0,8,0,8,0,8,0,16,0,8,1,12,0,16,1,8,0,8,0,16,0,8,0,8,0,8,0,8,1,16,0,16
%N a(n) is the cototient of n (A051953) iterated 4 times.
%C As iteration of A051953 progresses, powers of 2 may appear and it ends at fixed point 0. Analogous 4th iterates for A000005 or A000010 are A036452 and A049100.
%C It is assumed here that the value of A051953 at 0 is 0. - _Antti Karttunen_, Dec 22 2017
%H Antti Karttunen, <a href="/A053472/b053472.txt">Table of n, a(n) for n = 1..16384</a>
%e 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, n_4 = n_3 - Phi(n_3) = 12 - 4 = 8 so the 50th term is 8.
%t Array[Nest[# - EulerPhi@ # &, #, 4] &, 102] (* _Michael De Vlieger_, Dec 23 2017 *)
%o (PARI)
%o A051953(n) = if(!n,n,(n-eulerphi(n))); \\ With modification that returns zero for zero.
%o A053472(n) = A051953(A051953(A051953(A051953(n)))); \\ _Antti Karttunen_, Dec 22 2017
%Y Cf. A051953, A000005, A000010, A036452, A049100.
%Y Cf. A053470, A053471, A053473.
%K nonn
%O 1,18
%A _Labos Elemer_, Jan 14 2000
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