A053145 When cototient function (A051953) is iterated with initial value A002110(n), a(n) = number of iterations required to reach the stationary value=0.

2, 4, 7, 11, 17, 19, 30, 31, 40, 42, 60, 64, 79, 76, 94, 124, 130, 124, 156, 172, 139, 191, 194, 220, 212, 211, 260, 268, 276, 299, 295, 320, 335, 328, 357, 366, 378, 404, 427, 438, 437, 463, 476, 492, 505, 453, 490, 541, 563, 587, 542, 599, 638, 659

Offset

1,1

Links

Table of n, a(n) for n=1..54.

Formula

a(n) is smallest number such that Nest[A051953, A002110(n), a(n)]=0.

Example

n=6, A002110(6)=30030; the corresponding iteration chain is {30030, 24270, 17806, 9238, 4798, 2400, 1760, 1120, 736, 384, 256, 128, 64, 32, 16, 8, 4, 2, 1, 0}. Its length is 20, so a(6) = 20-1 = 19.

Mathematica

Array[-1 + Length@ NestWhileList[# - EulerPhi@ # &, Product[Prime@ i, {i, #}], # > 0 &] &, 30] (* Michael De Vlieger, Nov 20 2017 *)

Crossrefs

Cf. A002110, A051953.

Sequence in context: A146921 A153535 A116615 * A192589 A266448 A101978

Adjacent sequences: A053142 A053143 A053144 * A053146 A053147 A053148

Keyword

more,nonn

Author

Labos Elemer, Feb 28 2000

Extensions

More terms from Thomas Baruchel, Oct 11 2003

More terms from Sean A. Irvine, Dec 15 2021

Status

approved