A348182 a(1) = 1; for n >= 2, a(n) = 1 + a(A057022(n)).

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

Offset: 1

Author

Ctibor O. Zizka, Oct 05 2021

Keywords

• nonn

Comments

Number of steps needed to reach one when starting from k = n and repeatedly applying the map that replaces k by A057022(k). First maximal values for n = 1,2,3,5,11,29,61, .. which, except 1, are all primes (empirical result).

Examples

			a(5) = 1 + a(3) = 1 + 1 + a(2) = 1 + 1 + 1 + a(1) = 1 + 1 + 1 + 1 = 4.
		

Crossrefs

Cf. A057022.

Programs

Mathematica

a[1] = 1; a[n_] := a[n] = 1 + a[Floor[DivisorSigma[1, n]/DivisorSigma[0, n]]]; Array[a, 100] (* Amiram Eldar, Oct 05 2021 *)