Teerapat Srichan

Notes on Number Theory and Discrete Mathematics

Print ISSN 1310–5132, Online ISSN 2367–8275

Volume 24, 2018, Number 2, Pages 40—46

DOI: 10.7546/nntdm.2018.24.2.40-46

**Download full paper: PDF, 136 Kb**

## Details

### Authors and affiliations

Teerapat Srichan

*Department of Mathematics, Faculty of Science
Kasetsart University, Bangkok, Thailand
*

### Abstract

For a positive integer *q* > 1, we present the estimation of the average number of number of divisors of the sum of digits of squares. Moreover, we extend the result to the sum of digits of the power *h*, *h* ≥ 2.

### Keywords

- Divisor function
- Sum of digits

### 2010 Mathematics Subject Classification

- 11N37
- 11N69

### References

- Erdős, P. (1952) On the sum Σ
*d*(*f*(*k*)). Journal of the London Mathematical Society, 1.1, 7-15. - Drmota, M., Mauduit, C. & Rivat, J. (2011) The sum of digits function of polynomial sequences. Journal of the London Mathematical Society 84.1 , 81-102.
- Holleboom, L. J. (2014) Prime number decomposition of the Fourier transform of a function of the greatest common divisor. arXiv preprint arXiv:1410.2054 .
- Hooley, C. (1963) On the number of divisors of quadratic polynomials. Acta Mathematica, 110.1 , 97-114.
- Lapkova, K. (2016) Explicit upper bound for an average number of divisors of quadratic polynomials. Archiv der Mathematik, 106.3 , 247-256.
- Mauduit, C. & Rivat, J. (2009) La somme des chiffres des carrés. Acta Mathematica, 203.1, 107-148.
- Sándor, J. & Crstici, B. (2004) Handbook of Number Theory II. Kluwer Academic, Dordrecht (2004).
- Sándor, J., Mitrinovic, D.S. & Crstici, B. (2006) Handbook of Number Theory I. Springer, Netherlands.

## Related papers

## Cite this paper

Srichan, T. (2018). On the average number of divisors of the sum of digits of squares. Notes on Number Theory and Discrete Mathematics, 24(2), 40-46, doi: 10.7546/nntdm.2018.24.2.40-46.