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A053471
a(n) is the cototient of n (A051953) iterated 3 times.
4
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, 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, 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
OFFSET
1,10
COMMENTS
Iteration of A051953 behaves similarly to that of Euler Phi. Analogous 3rd iterates for A000005 or A000010 are A036455 and A049099.
It is assumed here that the value of A051953 at 0 is 0. - Antti Karttunen, Dec 22 2017
LINKS
EXAMPLE
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.
MATHEMATICA
Array[Nest[# - EulerPhi@ # &, #, 3] &, 95] (* Michael De Vlieger, Dec 23 2017 *)
PROG
(PARI)
A051953(n) = if(!n, n, (n-eulerphi(n))); \\ With modification that returns zero for zero.
A053471(n) = A051953(A051953(A051953(n))); \\ Antti Karttunen, Dec 22 2017
KEYWORD
nonn
AUTHOR
Labos Elemer, Jan 14 2000
STATUS
approved