We show that the fractional parts of the ratios n/ω(n), n/aω(n), n/τ(n) and n/aτ(n), where a ≥ 2 is a fixed integer and, as usual, ω(n) and τ(n) denote the number of prime divisors and the total number of divisors of n > 1, respectively, are uniformly distributed in the unit interval [0, 1]. This complements results of several authors about the scarcity of integral values taken by the above fractions.
|Number of pages||12|
|Journal||Uniform distribution theory|
|Publication status||Published - 2006|
- fractional part
- prime divisor
- uniform distribution