Geodesic
On a multiplicative partition function
The electronic journal of combinatorics, Tome 8 (2001) no. 1
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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.
DOI : 10.37236/1563
Classification : 11P82, 11N60, 05A18
Mots-clés : Stirling numbers, asymptotic analysis 
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     author = {Yifan Yang},
     title = {On a multiplicative partition function},
     journal = {The electronic journal of combinatorics},
     year = {2001},
     volume = {8},
     number = {1},
     doi = {10.37236/1563},
     zbl = {1022.11052},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/1563/}
}
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Yifan Yang. On a multiplicative partition function. The electronic journal of combinatorics, Tome 8 (2001) no. 1. doi: 10.37236/1563

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