A333870 The number of iterations of the absolute Möbius divisor function (A173557) required to reach from n to 1.

0, 1, 2, 1, 2, 2, 3, 1, 2, 2, 3, 2, 3, 3, 2, 1, 2, 2, 3, 2, 3, 3, 4, 2, 2, 3, 2, 3, 4, 2, 3, 1, 3, 2, 3, 2, 3, 3, 3, 2, 3, 3, 4, 3, 2, 4, 5, 2, 3, 2, 2, 3, 4, 2, 3, 3, 3, 4, 5, 2, 3, 3, 3, 1, 3, 3, 4, 2, 4, 3, 4, 2, 3, 3, 2, 3, 3, 3, 4, 2, 2, 3, 4, 3, 2, 4, 4

Offset: 1

Author

Amiram Eldar, Apr 08 2020

Keywords

• nonn

Comments

Apparently, the least number that reaches 1 after k iterations is A082449(k-1) (checked numerically for 1 <= k <= 17).

Examples

			a(3) = 2 since there are 2 iterations from 3 to 1: A173557(3) = 2 and A173557(2) = 1.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• Daeyeoul Kim, Umit Sarp, and Sebahattin Ikikardes, Iterating the Sum of Möbius Divisor Function and Euler Totient Function, Mathematics, Vol. 7, No. 11 (2019), pp. 1083-1094.

Crossrefs

Cf. A003434, A082449, A173557.

Programs

Mathematica

f[p_, e_] := p - 1; u[1] = 1; u[n_] := Times @@ (f @@@ FactorInteger[n]);a[n_] := Length @ FixedPointList[u, n] - 2; Array[a, 100]