A053472 a(n) is the cototient of n (A051953) iterated 4 times.

0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 4, 0, 2, 0, 4, 0, 4, 0, 4, 0, 4, 0, 8, 0, 4, 1, 4, 0, 4, 0, 8, 0, 4, 0, 8, 0, 4, 1, 8, 0, 8, 0, 4, 1, 4, 0, 8, 0, 8, 0, 8, 0, 8, 0, 8, 0, 8, 0, 16, 0, 8, 1, 12, 0, 16, 1, 8, 0, 8, 0, 16, 0, 8, 0, 8, 0, 8, 0, 8, 1, 16, 0, 16

Offset: 1

Author

Labos Elemer, Jan 14 2000

Keywords

• nonn

Comments

As iteration of A051953 progresses, powers of 2 may appear and it ends at fixed point 0. Analogous 4th iterates for A000005 or A000010 are A036452 and A049100.

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 so the 50th term is 8.
		

Links

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

Crossrefs

Cf. A051953, A000005, A000010, A036452, A049100.

Cf. A053470, A053471, A053473.

Programs

Mathematica

Array[Nest[# - EulerPhi@ # &, #, 4] &, 102] (* Michael De Vlieger, Dec 23 2017 *)

PARI

A051953(n) = if(!n,n,(n-eulerphi(n))); \\ With modification that returns zero for zero.
A053472(n) = A051953(A051953(A051953(A051953(n)))); \\ Antti Karttunen, Dec 22 2017