A060607 - OEIS

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

(list; graph; refs; listen; history; text; internal format)

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