Harshad Number - Estimating The Density of Harshad Numbers

Estimating The Density of Harshad Numbers

If we let N(x) denote the number of Harshad numbers ≤ x, then for any given ε > 0,

as shown by Jean-Marie De Koninck and Nicolas Doyon; furthermore, De Koninck, Doyon and Kátai proved that

where c = (14/27) log 10 ≈ 1.1939.

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