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On the distribution of the number of digits needed to write the factorization of an integer. (English) Zbl 1174.11072

Let \(F_g(n)\) be the number of digits needed to write the prime factorization of \(n\) in base \(g\). The main result states that the central distribution of the function \(F_g(n)\) is Gaussian. An upper bound and a lower bound for the valves of \(F_g(n)\) are given in terms of \(n\), \(g\) and the number \(\omega(n)\) of distinct prime factors of \(n\).

MSC:

11N37 Asymptotic results on arithmetic functions
11A63 Radix representation; digital problems
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