The relationship between Liouville's arithmetic identities and products of Lambert series is investigated. For example it is shown that Liouville's arithmetic formula for the sum where n ∈ N and F: Z → C is an even function, is equivalent to the Lambert series for given by Ramanujan.

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Keywords Lambert series, Liouville's identities, Ramanujan's identity
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Journal Dissertationes Mathematicae
Alaca, A, Alaca, S, McAfee, E., & Williams, K.S. (2007). Lambert series and Liouville's identities. Dissertationes Mathematicae, (445), 5–72. doi:10.4064/dm445-0-1