Abstract
Let a( n) denote the number of nonisomorphic Abelian groups with n elements. Several problems concerning a( n) and a class of related multiplicative functions are discussed. These include precise characterizations of local densities, distribution of values (where the Tauberian theorem of Hardy-Ramanujan is used), sharp formulas for the sums Σ n≤ x F( a( n)) for a wide class of functions F, and a comparison of values taken on the average by a( n) and some other common arithmetic functions.
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