A053470 a(n) is the cototient of n (A051953) iterated twice.

0, 0, 0, 1, 0, 2, 0, 2, 1, 4, 0, 4, 0, 4, 1, 4, 0, 8, 0, 8, 3, 8, 0, 8, 1, 8, 3, 8, 0, 12, 0, 8, 1, 12, 1, 16, 0, 12, 7, 16, 0, 22, 0, 16, 9, 16, 0, 16, 1, 22, 1, 16, 0, 24, 7, 16, 9, 22, 0, 24, 0, 16, 9, 16, 1, 24, 0, 24, 5, 24, 0, 32, 0, 20, 11, 24, 1, 36, 0, 32, 9, 30, 0, 44, 9, 24, 1, 32, 0

Offset: 1

Author

Labos Elemer, Jan 14 2000

Keywords

• nonn

Comments

Iteration of A051953 is ended at fixed point 0. Analogous 2nd iterates for number of divisors (A000005) and Euler-Phi (A000010) are A036454 and A010554.

Examples

			n=50, n_1 = n - phi(n) = 50 - 20 = 30, n_2 = n_1 - Phi(n_1) = 30 - 8 = 22, so the 50th term is 22.
		

Links

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

Crossrefs

Cf. A051953, A000005, A000010, A036454, A010554.

Cf. A053471, A053472, A053473.

Programs

Mathematica

Array[Nest[# - EulerPhi@ # &, #, 2] &, 89] (* Michael De Vlieger, Dec 23 2017 *)

PARI

A051953(n) = (n-eulerphi(n));
A053470(n) = if(1==n,0,A051953(A051953(n))); \\ Antti Karttunen, Dec 22 2017

Formula

a(1) = 0; for n > 1, a(n) = A051953(A051953(n)).