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

1,6

Comments

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

Links

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

Formula

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

Example

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.

Mathematica

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

Prog

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

Crossrefs

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

Cf. A053471, A053472, A053473.

Sequence in context: A361850 A295689 A305804 * A308202 A329152 A368581

Adjacent sequences: A053467 A053468 A053469 * A053471 A053472 A053473

Keyword

nonn

Author

Labos Elemer, Jan 14 2000

Status

approved