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

Author

Labos Elemer, Feb 28 2000

Keywords

• more
• nonn

Examples

			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.
		

Crossrefs

Cf. A002110, A051953.

Programs

Mathematica

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

Formula

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

Extensions

More terms from Thomas Baruchel, Oct 11 2003

More terms from Sean A. Irvine, Dec 15 2021