

A330877


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).


0



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, 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, 10, 23, 11, 23, 10, 22, 12, 21, 24, 21, 12, 21, 13
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OFFSET

0,2


COMMENTS

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.


LINKS

Table of n, a(n) for n=0..68.


EXAMPLE

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


CROSSREFS

Cf. A000005, A155043, A261085, A261088.
Cf. A049820, A062249.
Sequence in context: A257699 A160535 A258235 * A021050 A194797 A255138
Adjacent sequences: A330874 A330875 A330876 * A330878 A330879 A330880


KEYWORD

nonn


AUTHOR

Ctibor O. Zizka, Apr 29 2020


STATUS

approved



