[seqfan] Re: Concerns about some recent comments by Jaroslav Krizek

Douglas McNeil mcneil at hku.hk
Tue Jun 15 03:40:11 CEST 2010

> It seems that he just wants the world to know his
> "Conjecture: There are no numbers n such that all their means A, B, G, H
> and K are integers".

Looks like there are a couple of conjecture variants.

The A000217 version I think is false as written because n=1 works.

But if you exclude the trivial counterexample, isn't it true instead?
Consider G(n)= factorial(n)**(1/n).  Then G^n = factorial(n).  Count
factors of 2 on the rhs (cf. A011371); this number is always > 0 and <
n for n > 1, so there are never the right number of 2s for
factorial(n) to be an nth power.  Aren't A, B, H, and K irrelevant?

What am I missing?


Department of Earth Sciences
University of Hong Kong

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