Abstract
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.
| Original language | English |
|---|---|
| Pages (from-to) | 15-26 |
| Number of pages | 12 |
| Journal | Uniform distribution theory |
| Volume | 1 |
| Issue number | 1 |
| Publication status | Published - 2006 |
Keywords
- sequence
- fractional part
- divisor
- prime divisor
- uniform distribution