An asymptotic formula for the generalized exponential divisor function. (English) Zbl 1349.11132
Summary: Let \(\tau^{(e)} (n)\) denote the number of exponential divisor of \(n\). Similar to the generalization from \(d(n)\) to \(d_k^{(n)}, \tau^{(e)}(n)\) can be extended to \(\tau k^{(e)}(n)\). It is determined that the function \(\tau_3^{(e)}(n)\) has an asymptotic formula in a short interval.
MSC:
11N37 | Asymptotic results on arithmetic functions |
11A25 | Arithmetic functions; related numbers; inversion formulas |