A053471 - OEIS

%I #15 May 31 2018 02:09:09

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

%C Iteration of A051953 behaves similarly to that of Euler Phi. Analogous 3rd iterates for A000005 or A000010 are A036455 and A049099.

%C It is assumed here that the value of A051953 at 0 is 0. - _Antti Karttunen_, Dec 22 2017

%H Antti Karttunen, <a href="/A053471/b053471.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 so the 50th term is 12.

%t Array[Nest[# - EulerPhi@ # &, #, 3] &, 95] (* _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 A053471(n) = A051953(A051953(A051953(n))); \\ _Antti Karttunen_, Dec 22 2017

%Y Cf. A051953, A000005, A000010, A036455, A049099.

%Y Cf. A053470, A053472, A053473.

%K nonn

%O 1,10

%A _Labos Elemer_, Jan 14 2000