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The electronegativity (identified with the negative of the chemical potential) of atoms and ions has been calculated in several isoelectronic series using the Density Functional Theory. Then, the electronegativities of atoms and ions with fractional nuclear charge have been obtained by interpolation in each isoelectronic series. Similar interpolations have been performed, starting with approximate electronegativities obtained by Mulliken's finite difference approximation. Both sets of results have been compared.