[math-fun] Re: Divisor chains

3 May 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

[math-fun] Re: Divisor chains

Edwin Clark