A053473 a(n) is the cototient of n (A051953) iterated 5 times.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 2, 0, 1, 0, 2, 0, 2, 0, 2, 0, 2, 0, 4, 0, 2, 0, 2, 0, 2, 0, 4, 0, 2, 0, 4, 0, 2, 0, 4, 0, 4, 0, 2, 0, 2, 0, 4, 0, 4, 0, 4, 0, 4, 0, 4, 0, 4, 0, 8, 0, 4, 0, 8, 0, 8, 0, 4, 0, 4, 0, 8, 0, 4, 0, 4, 0, 4, 0, 4, 0, 8, 0, 8, 0, 4, 1

Offset: 1

Author

Labos Elemer, Jan 14 2000

Keywords

• nonn

Comments

As iteration of A051953 progresses, more and more powers of 2 and 0 appear. The fixed point is 0. Analogous 5th iterates for A000005 or A000010 are A036453 and A049107.

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, n_4 = n_3 - Phi(n_3) = 12 - 4 = 8, n_5 = 8 - Phi(8) = 4 so the 50th term is 4.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537

Crossrefs

Cf. A051953, A000005, A000010, A036453, A049107.

Cf. A053470, A053471, A053472.

Programs

Mathematica

a[n_] := Nest[# - EulerPhi[#]&, n, 5];
Array[a, 105] (* Jean-François Alcover, Dec 26 2017 *)

PARI

A051953(n) = if(!n,n,(n-eulerphi(n))); \\ With modification that returns zero for zero.
A053473(n) = A051953(A051953(A051953(A051953(A051953(n))))); \\ Antti Karttunen, Dec 22 2017