A348182 - OEIS

%I #10 Oct 09 2021 16:03:35

%S 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,

%T 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,

%U 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

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

%C 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).

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

%t a[1] = 1; a[n_] := a[n] = 1 + a[Floor[DivisorSigma[1, n]/DivisorSigma[0, n]]]; Array[a, 100] (* _Amiram Eldar_, Oct 05 2021 *)

%Y Cf. A057022.

%K nonn

%O 1,2

%A _Ctibor O. Zizka_, Oct 05 2021