On a Multiplicative Partition Function
Copyright policy )On a Multiplicative Partition Function
Let $D(s)=\sum^\infty_{m=1}a_mm^{-s}$ be the Dirichlet series generated by the infinite product $\prod^\infty_{k=2}(1-k^{-s})$. The value of $a_m$ for squarefree integers $m$ with $n$ prime factors depends only on the number $n$, and we let $f(n)$ denote this value. We prove an asymptotic estimate for $f(n)$ which allows us to solve several problems raised in a recent paper by M. V. Subbarao and A. Verma.
Distribution functions associated with additive and positive multiplicative functions, asymptotic analysis, Partitions of sets, Analytic theory of partitions, Stirling numbers
Distribution functions associated with additive and positive multiplicative functions, asymptotic analysis, Partitions of sets, Analytic theory of partitions, Stirling numbers
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