[seqfan] Re: Xmas-challenge

David Corneth davidacorneth at gmail.com
Sun Dec 27 16:00:23 CET 2020


Just some thoughts and naive observations. Most of these quotients are
primes. A few are prime powers. Then some other stuff.
Looking at the lcm of elements in that length 76 solution
it's 6064949221531200 which is in A025487. Would it help predict the lcm of
such a solution and take it's divisors <= n to see where that gets us?



On Sun, Dec 27, 2020 at 1:32 PM Peter Luschny <peter.luschny at gmail.com>
wrote:

> Andrew Weimholt> ... here one of length 72 - probably not the max.
>
> This one has length 76:
> [93, 31, 62, 1, 87, 29, 58, 2, 92, 46, 23, 69, 3, 57, 19, 38, 76, 4, 68,
> 34, 17, 85, 5, 35, 70, 10, 50, 25, 75, 15, 45, 90, 30, 60, 20, 40, 80, 16,
> 64, 32, 96, 48, 24, 12, 6, 78, 26, 52, 13, 91, 7, 49, 98, 14, 56, 28, 84,
> 42, 21, 63, 9, 81, 27, 54, 18, 36, 72, 8, 88, 44, 22, 66, 33, 99, 11, 55]
>
> Can we characterize the elements of the complement?
> {37,39,41,43,47,51,53,59,61,65,67,71,73,74,77,79,82,83,86,89,94,95,97}
>
> These are all primes or semiprimes. Note that in Andrew's
> sequences there is also 2*5*7 in the complement set. Can one
> understand this as an indication of non-optimality?
>
> Is the longest chain unique? Probably not. In this case I
> will register the sequence: "Number of divisor chains with
> maximum length".
>
> But one of the correspondents noted that there is uniqueness
> in certain cases. However, it is not clear which these are.
>
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>



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