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

1,10

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

Links

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

Example

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.

Mathematica

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

Prog

(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

Crossrefs

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

Cf. A053470, A053472, A053473.

Sequence in context: A181587 A096158 A264782 * A144078 A277158 A318282

Adjacent sequences: A053468 A053469 A053470 * A053472 A053473 A053474

Keyword

nonn

Author

Labos Elemer, Jan 14 2000

Status

approved