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In this note, basing on a certain functional equation of the dilogarithmfunction, we establish nontrivial lower bounds for the $p$-adic valuation(where $p$ is a given prime number) of some type of rational numbers involvingharmonic numbers. Then we use our estimate to derive the integrality of somesequences of rational numbers, which cannot be seen directly from theirdefinitions.

Nontrivial lower bounds for the $p$-adic valuations of some type of  rational numbers and an application for establishing the integrality of some  rational sequences