Debika Banerjee and Makoto Minamide

Notes on Number Theory and Discrete Mathematics

Print ISSN 1310–5132, Online ISSN 2367–8275

Volume 22, 2016, Number 1, Pages 8—17

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## Details

### Authors and affiliations

Debika Banerjee

*Harish-Chandra Research Institute
Chhatnag Road, Jhunsi, Allahabad 211019, India
*

Makoto Minamide

*Faculty of Science, Yamaguchi University*

Yoshida 1677-1, Yamaguchi 753–8512, Japan

Yoshida 1677-1, Yamaguchi 753–8512, Japan

### Abstract

In this paper, let *p* denote a prime. We shall consider sums of the type Φ (*x,y;f*)= Σ* _{n≤p|n ⇒ p > y} f(n)* and ψ (

*x,y;f*)=Σ

*for certain kinds of arithmetical functions*

_{n≤p|n ⇒ p < y}f(n)*f*and prove some identities for Φ and ψ which are analogous to the ‘so-called’ Buchstab identity. As an application, we will prove some formulas for square-free integers.

### Keywords

- Buchstab’s identity
- Square-free integers

### AMS Classification

- 11N25
- 11N37

### References

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Hungarica, 20, 189–192. - Tenenmbaum, G. (1995) Introduction to Analytic and Probabilistic Number Theory, Cambridge Studies in Advanced Mathematics, Vol. 46, Cambridge University Press.

## Related papers

## Cite this paper

APABanerjee, D. & Makoto M. (2016). On an analogue of Buchstab’s identity. Notes on Number Theory and Discrete Mathematics, 22(1), 8-17.

ChicagoBanerjee, Debika, and Makoto Minamide. “On an Analogue of Buchstab’s Identity.” Notes on Number Theory and Discrete Mathematics 22, no. 1 (2016): 8-17.

MLABanerjee, Debika, and Makoto Minamide. “On an Analogue of Buchstab’s Identity.” Notes on Number Theory and Discrete Mathematics 22.1 (2016): 8-17. Print.