Dividing n consecutive integers by (1,2,3,...,n)

[Don Reble]

> Don, could you please shed some light on how you got all these values?

    I test each integer in turn, to see whether it's the value.
    Just careful coding in a machine-friendly language.

> Can your approach help to compute more values?

    Yeah, I could have run the program longer.

> It turns out that there are no so many feasible permutations, their
> number for n=1,...,16 is:
>
> 1, 2, 6, 8, 48, 24, 216, 120, 240, 128, 2544, 336, 11520, 3168, 1536, 480

    Furthermore, sometimes two permutations map onto the same starting
    point, modulo lcm(1..n). The number of starting points is
1, 2, 5, 8, 32, 11, 72, 64, 66, 17, 213, 37, 417, 120, 67, 60, 694, 217

    That's a good way to find all solutions; but if you want only the
    least solution, it may be a waste of time.

-- 
Don Reble  djr at nk.ca


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