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%I #18 May 31 2024 22:10:48
%S 0,0,0,1,0,2,0,2,1,4,0,4,0,4,1,4,0,8,0,8,3,8,0,8,1,8,3,8,0,12,0,8,1,
%T 12,1,16,0,12,7,16,0,22,0,16,9,16,0,16,1,22,1,16,0,24,7,16,9,22,0,24,
%U 0,16,9,16,1,24,0,24,5,24,0,32,0,20,11,24,1,36,0,32,9,30,0,44,9,24,1,32,0
%N a(n) is the cototient of n (A051953) iterated twice.
%C Iteration of A051953 is ended at fixed point 0. Analogous 2nd iterates for number of divisors (A000005) and Euler-Phi (A000010) are A036454 and A010554.
%H Antti Karttunen, <a href="/A053470/b053470.txt">Table of n, a(n) for n = 1..16384</a>
%F a(1) = 0; for n > 1, a(n) = A051953(A051953(n)).
%e n=50, n_1 = n - phi(n) = 50 - 20 = 30, n_2 = n_1 - Phi(n_1) = 30 - 8 = 22, so the 50th term is 22.
%t Array[Nest[# - EulerPhi@ # &, #, 2] &, 89] (* _Michael De Vlieger_, Dec 23 2017 *)
%o (PARI)
%o A051953(n) = (n-eulerphi(n));
%o A053470(n) = if(1==n,0,A051953(A051953(n))); \\ _Antti Karttunen_, Dec 22 2017
%Y Cf. A051953, A000005, A000010, A036454, A010554.
%Y Cf. A053471, A053472, A053473.
%K nonn,changed
%O 1,6
%A _Labos Elemer_, Jan 14 2000
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