A330877 - OEIS

%I #20 May 16 2020 03:36:40

%S 0,2,1,7,3,6,2,5,4,4,3,12,3,11,4,10,13,10,4,9,5,8,5,8,14,7,6,32,6,32,

%T 6,31,7,30,7,29,33,29,8,28,8,28,8,27,9,26,9,12,9,11,10,25,10,25,10,24,

%U 10,23,11,23,10,22,12,21,24,21,12,21,13

%N Number of steps needed to reach zero or a cycle when starting from k = n and repeatedly applying the map that replaces k by k - d(k) if k is even, by k + d(k) if k is odd, where d(k) is the number of divisors of k (A000005).

%C First cycle we see for n = 83. The length of the cycle is 38 steps. To reach a cycle means the time to first step into the loop.

%e n = 1, mapping steps are 1 + 1 = 2, 2 - 2 = 0, a(1) = 2;

%e n = 2, mapping steps are 2 - 2 = 0, a(2) = 1;

%e n = 3, mapping steps are 3 + 2 = 5, 5 + 2 = 7, 7 + 2 = 9, 9 + 3 = 12, 12 - 6 = 6, 6 - 4 = 2, 2 - 2 = 0, a(3) = 7;

%e n = 4, mapping steps are 4 - 3 = 1, 1 + 1 = 2, 2 - 2 = 0, a(4) = 3;

%e n = 5, mapping steps are 5 + 2 = 7, 7 + 2 = 9, 9 + 3 = 12, 12 - 6 = 6, 6 - 4 = 2, 2 - 2 = 0, a(5) = 6.

%Y Cf. A000005, A155043, A261085, A261088.

%Y Cf. A049820, A062249.

%K nonn

%O 0,2

%A _Ctibor O. Zizka_, Apr 29 2020