Divisor chains
Edwin Clark
eclark at math.usf.edu
Tue May 4 03:52:12 CEST 2004
On Mon, 3 May 2004, Richard Guy wrote:
> The following might be an acceptable sequence
> for Neil Sloane's OEIS, but someone needs to
> do some work
>
> 1 2 3 4 5 6 7 8 9 10 11 12 13 14 ...
> 1 1 1 1 1 1 1 5 4 1 2 5 5 4 ...
>
I compute up to n = 19 the following number of divisor chains:
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
1 1 1 1 1 1 1 5 4 3 2 8 4 6 47 44 6 37 6
which differs from your values at 10, 12, 13, 14.
It's interesting that a(15) > a(16). One might think powers of 2 would
give larger values.
If anyone cares to check my chains from 10 to 16 here they are:
10 2 4 8 6 5 7 3 9 1
10 2 4 8 3 9 6 7 1 5
10 2 6 3 7 4 8 5 9 1
11 1 4 8 6 10 5 9 2 7 3
11 1 2 7 3 8 4 9 5 10 6
12 3 5 10 2 1 11 4 8 7 9 6
12 2 7 1 11 3 9 5 10 4 8 6
12 2 7 3 8 4 9 5 10 6 11 1
12 4 8 3 9 6 2 11 5 10 7 1
12 4 8 6 10 5 9 2 7 3 11 1
12 6 9 3 2 8 4 11 5 10 7 1
12 3 5 10 2 8 4 11 1 7 9 6
12 2 1 5 10 3 11 4 8 7 9 6
13 1 2 8 6 10 4 11 5 3 9 12 7
13 1 2 8 6 10 4 11 5 12 9 3 7
13 1 2 8 12 4 10 5 11 6 9 3 7
13 1 2 8 3 9 4 10 5 11 6 12 7
14 2 8 6 10 4 11 5 3 9 12 7 13 1
14 2 8 6 10 4 11 5 12 9 3 7 13 1
14 2 8 3 9 12 4 13 1 11 7 6 10 5
14 2 8 3 9 4 10 5 11 6 12 7 13 1
14 2 8 12 4 10 5 11 6 9 3 7 13 1
14 2 8 12 9 3 4 13 1 11 7 6 10 5
15 3 2 1 7 14 6 4 13 5 10 8 11 9 12
15 5 10 6 12 8 14 7 11 2 9 1 4 13 3
15 5 4 3 9 12 2 10 6 11 1 13 7 14 8
15 5 4 2 13 1 8 12 3 7 14 6 9 11 10
15 5 10 3 11 4 12 2 1 9 6 13 7 14 8
15 5 10 3 11 4 6 9 7 14 12 8 13 1 2
15 3 6 4 14 7 1 10 5 13 2 8 11 9 12
15 3 2 4 12 9 5 10 6 11 1 13 7 14 8
15 1 2 9 3 10 4 11 5 12 6 13 7 14 8
15 5 10 3 11 1 9 6 12 4 2 13 7 14 8
15 5 4 12 9 3 2 10 6 11 1 13 7 14 8
15 1 4 2 11 3 9 5 10 12 6 13 7 14 8
15 1 8 12 6 2 11 5 10 14 7 13 4 9 3
15 5 10 2 1 11 4 6 9 7 14 12 8 13 3
15 3 6 4 14 7 1 2 13 5 10 8 11 9 12
15 5 10 6 3 13 4 7 9 12 14 1 11 2 8
15 5 10 2 4 9 3 12 6 11 1 13 7 14 8
15 5 4 2 13 3 6 1 7 14 10 8 11 9 12
15 5 10 3 11 1 9 2 4 12 6 13 7 14 8
15 5 10 6 3 13 4 14 7 11 8 12 9 1 2
15 5 4 2 13 1 8 6 9 7 14 12 3 11 10
15 5 10 6 9 3 4 13 1 11 7 12 2 14 8
15 5 10 6 2 1 13 4 14 7 11 8 12 9 3
15 5 1 7 2 6 3 13 4 14 10 8 11 9 12
15 5 10 2 4 12 6 9 3 11 1 13 7 14 8
15 5 4 2 13 3 14 7 1 8 12 6 9 11 10
15 5 10 6 12 4 2 9 3 11 1 13 7 14 8
15 5 4 2 13 3 6 8 7 9 12 14 1 11 10
15 5 10 6 12 8 14 7 11 2 1 13 4 9 3
15 5 10 6 3 13 4 14 7 11 8 2 1 9 12
15 3 9 1 2 10 4 11 5 12 6 13 7 14 8
15 5 10 6 9 3 8 14 7 11 2 1 13 4 12
15 1 2 3 7 14 6 4 13 5 10 8 11 9 12
15 1 8 12 9 5 10 6 11 7 14 2 4 13 3
15 5 10 6 3 13 4 8 2 11 7 14 1 9 12
15 5 10 6 9 3 12 4 2 11 1 13 7 14 8
15 5 10 2 1 11 4 12 3 9 6 13 7 14 8
15 5 2 11 3 6 14 7 9 8 10 1 13 4 12
15 5 10 3 11 4 8 14 2 6 13 7 1 9 12
15 5 10 6 2 1 13 4 14 7 11 8 3 9 12
15 3 9 1 14 6 4 13 5 7 11 8 12 2 10
15 3 6 12 9 5 10 4 2 11 1 13 7 14 8
15 1 8 3 9 6 2 11 5 10 14 7 13 4 12
15 5 4 12 9 3 8 14 2 6 13 7 1 11 10
15 3 2 10 5 7 14 8 1 13 6 4 11 9 12
15 5 10 6 3 13 4 14 7 1 2 8 11 9 12
15 5 4 3 9 12 8 14 2 6 13 7 1 11 10
16 4 10 15 3 2 5 11 6 12 7 13 8 14 9 1
16 2 6 12 9 5 10 15 3 13 7 14 8 1 11 4
16 8 12 9 5 10 6 11 7 14 2 4 13 3 15 1
16 8 12 9 5 10 15 3 13 7 1 11 2 14 6 4
16 8 3 9 6 2 11 5 10 14 7 13 4 12 15 1
16 8 12 9 15 10 5 3 13 7 14 2 6 1 11 4
16 8 12 9 5 10 15 3 13 7 14 2 6 1 11 4
16 2 6 4 14 3 15 10 7 11 8 12 9 13 5 1
16 8 6 15 9 2 14 5 3 13 7 1 11 10 12 4
16 4 2 11 3 9 5 10 12 6 13 7 14 8 15 1
16 2 9 3 10 4 11 5 12 6 13 7 14 8 15 1
16 2 9 3 15 5 10 12 6 13 7 14 8 1 11 4
16 8 12 6 2 11 5 10 14 7 13 4 9 3 15 1
16 8 2 13 3 14 7 9 12 6 15 5 10 1 11 4
16 8 2 13 1 5 15 3 7 14 6 9 11 10 12 4
16 2 6 12 9 15 10 5 3 13 7 14 8 1 11 4
16 8 12 3 13 2 9 7 14 6 15 5 10 1 11 4
16 2 9 3 15 5 10 6 11 1 13 7 14 8 12 4
16 8 2 13 3 6 1 7 14 5 15 9 11 10 12 4
16 8 6 3 11 4 12 5 13 2 10 15 7 14 9 1
16 8 12 3 13 4 14 5 15 9 11 10 6 7 1 2
16 8 12 3 13 4 14 7 11 2 15 5 10 6 9 1
16 8 12 9 15 5 13 6 14 7 3 2 10 1 11 4
16 8 3 9 12 2 10 5 13 6 14 7 15 1 11 4
16 8 3 9 6 2 11 5 10 14 7 13 1 15 12 4
16 4 10 15 3 8 14 7 11 2 6 12 9 13 5 1
16 2 3 7 14 6 4 13 5 10 8 11 9 12 15 1
16 8 4 14 3 15 10 7 11 2 6 12 9 13 5 1
16 2 9 3 10 5 15 6 11 1 13 7 14 8 12 4
16 8 2 13 3 14 7 9 12 6 10 5 15 1 11 4
16 8 12 9 3 2 10 5 13 6 14 7 15 1 11 4
16 8 2 13 1 10 5 11 6 9 3 14 7 15 12 4
16 8 12 3 13 2 9 7 14 6 10 5 15 1 11 4
16 8 12 9 15 10 5 3 13 7 1 11 2 14 6 4
16 4 10 15 9 2 14 7 11 8 12 6 3 13 5 1
16 8 4 14 6 12 10 7 11 2 15 3 9 13 5 1
16 2 9 3 10 8 12 5 13 6 14 7 15 1 11 4
16 4 10 6 12 8 14 7 11 2 15 3 9 13 5 1
16 8 12 3 13 4 14 7 11 2 10 5 15 6 9 1
16 4 10 15 3 6 2 14 7 11 8 12 9 13 5 1
16 2 9 3 10 5 15 12 6 13 7 14 8 1 11 4
16 4 2 11 3 9 15 12 6 13 7 14 8 10 5 1
16 8 12 6 14 4 10 7 11 2 15 3 9 13 5 1
16 8 12 9 15 6 11 7 14 2 4 13 3 10 5 1
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