A053475 1 + the number of iterations of A051953 (Euler-cototient) function needed to reach 0, starting at n.

2, 3, 3, 4, 3, 5, 3, 5, 4, 6, 3, 6, 3, 6, 4, 6, 3, 7, 3, 7, 5, 7, 3, 7, 4, 7, 5, 7, 3, 8, 3, 7, 4, 8, 4, 8, 3, 8, 5, 8, 3, 9, 3, 8, 6, 8, 3, 8, 4, 9, 4, 8, 3, 9, 5, 8, 6, 9, 3, 9, 3, 8, 6, 8, 4, 9, 3, 9, 5, 9, 3, 9, 3, 9, 5, 9, 4, 10, 3, 9, 6, 10, 3, 10, 6, 9, 4, 9, 3, 10, 4, 9, 5, 9, 4, 9, 3, 9, 6, 10, 3, 10

Offset: 1

Author

Labos Elemer, Jan 14 2000

Keywords

• nonn

Comments

Analogous sequences of iteration-lengths for A000005 or A000010 are A036459 and A049108 resp. The length values of 3 occur if the initial value is prime resulting in {p,1,0} iterations.

Examples

			Starting with n=18, the iterations of A051953 are as follows: {18,12,8,4,2,1,0}. The length of this sequence is 7, so a(18) = 7. The function is applied a(n)-1 times.
		

Links

• T. D. Noe, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000005, A000010, A051953, A036459, A049108, A076640.

Programs

Mathematica

Table[Length@ NestWhileList[# - EulerPhi@ # &, n, # > 0 &], {n, 84}] (* Michael De Vlieger, Jul 04 2016 *)

Formula

a(n) = A076640(n) + 1. - Michael De Vlieger, Jul 04 2016