Number of unrestricted divisor chains

[Eugene McDonnell]

The number of divisor chains having any first digit:

k    1 2 3 4 5 6 7 8  9 10 11 12 13 14  15  16  17  18  19   20   21   
22   23    24
a(k) 1 1 2 2 4 5 7 7 24 22 29 39 67 55 386 235 312 347 451 1319 5320 
3220 4489 20237

For example, the five unrestricted divisor chains of length 6 are:

4 1 5 2 6 3
4 2 6 3 5 1
5 1 2 4 6 3
5 1 6 4 2 3
6 2 4 3 5 1

There appear to be very few chains beginning with 1, 2, 3 and 5.

Eugene McDonnell
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