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

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

Author

Labos Elemer, Jan 14 2000

Keywords

• nonn

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

Examples

			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.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..16384

Crossrefs

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

Cf. A053470, A053472, A053473.

Programs

Mathematica

Array[Nest[# - EulerPhi@ # &, #, 3] &, 95] (* Michael De Vlieger, Dec 23 2017 *)

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