A060607 Number of iterations of phi(x) at prime(n) needed to reach 1.

1, 2, 3, 3, 4, 4, 5, 4, 5, 5, 5, 5, 6, 5, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 6, 7, 6, 7, 8, 7, 7, 7, 7, 6, 8, 7, 8, 7, 7, 8, 7, 7, 7, 7, 8, 7, 8, 8, 8, 8, 9, 8, 8, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 8, 8, 7, 8, 9, 8, 9, 9, 8, 8, 8, 8, 8, 9, 9, 8, 9, 8, 9, 9, 7, 8, 9, 9, 8, 9, 8, 8, 8, 9, 9, 9, 8

Offset

1,2

Comments

Indices of records in this sequence: 1, 2, 3, 5, 7, 13, 23, 33, 55, 116, 184, 384, 719, 1323, 2010, 4289, 6543, 13044, 25685, 45859, 92479, 175261, 298106, 636606, ... The records appear to be A000027. - Michael De Vlieger, Mar 27 2019.

Links

Michael De Vlieger, Table of n, a(n) for n = 1..10000

Formula

a(n) = A003434(A000040(n)). [corrected by Michel Marcus, Mar 27 2019]

Mathematica

Array[-1 + Length@ NestWhileList[EulerPhi, Prime@ #, # > 1 &] &, 105] (* Michael De Vlieger, Mar 27 2019 *)

Prog

(PARI) a(n) = my(t=0, p=prime(n)); while(p>1, t++; p=eulerphi(p)); t; \\ Michel Marcus, Mar 27 2019

Crossrefs

Cf. A000040, A000010, A049108, A003434.

Sequence in context: A297025 A325134 A218007 * A265690 A061339 A073933

Adjacent sequences: A060604 A060605 A060606 * A060608 A060609 A060610

Keyword

easy,nonn

Author

Labos Elemer, Apr 13 2001

Extensions

Name edited by Michel Marcus, Mar 27 2019

Status

approved