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I define $\nu(n)$ the number of different factorizations for an integer $n$. I know there are papers about $\delta(n)$ the number of dividers for an integer $n$ (Landau, Euler, Dirichlet) but I still found nothing about $\nu(n)$.

Has someone any idea of a limit for $\nu(n)$ as $n\to\infty$ ?

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    $\begingroup$ What exactly do you mean with "factorizations"? Do $6=2\cdot 3=3\cdot 2$ count as different factorizations? Do $6=2\cdot 3=1\cdot 2\cdot 3$? $\endgroup$
    – Wojowu
    Commented Jan 4, 2022 at 15:02
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    $\begingroup$ Maybe you are looking for oeis.org/A001055 "The multiplicative partition function: number of ways of factoring $n$ with all factors greater than $1$." $\endgroup$
    – Gerry Myerson
    Commented Jan 4, 2022 at 15:36

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