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On an asymptotic formula for the Niven numbers. (English) Zbl 0582.10007

The positive integer n is called a Niven number, if n is divisible by its digital sum s(n). For fixed \(k\in {\mathbb{N}}\) the authors deduce the asymptotic formula \(N_ k(x)\sim c_ k \log^ k x\) \((x\to \infty)\), where \(N_ k(x):=\#\{n\in {\mathbb{N}}:\) \(n\leq x,\quad s(n)=k\) and \(s(n)| n\}.\)
Reviewer: W.Recknagel

MSC:

11B39 Fibonacci and Lucas numbers and polynomials and generalizations
11N37 Asymptotic results on arithmetic functions
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