## 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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