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 Post subject: Is it an integer?
PostPosted: Wed Aug 30, 2017 6:50 pm 
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Investigating something on the serieses with Harmonic numbers the following occured. I do not have a solution , yet I would like to see one.

Let $n \geq 1$ and denote as $\mathcal{H}_n$ the $n$ - th harmonic number. Let us also denote as ${\rm lcm} ( \cdot , \cdot )$ the least common multiple. Is it true that the sequence defined as

$$a_n=n^{\mathcal{H}_n {\rm lcm}(1,2,\dots,n)}$$

is an integer, that is contains also integer numbers?

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