On the average number of divisors of the sum of digits of squares

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
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

1. Erdős, P. (1952) On the sum Σ d(f(k)). Journal of the London Mathematical Society, 1.1, 7-15.
2. 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.
3. Holleboom, L. J. (2014) Prime number decomposition of the Fourier transform of a function of the greatest common divisor. arXiv preprint arXiv:1410.2054 .
4. Hooley, C. (1963) On the number of divisors of quadratic polynomials. Acta Mathematica, 110.1 , 97-114.
5. Lapkova, K. (2016) Explicit upper bound for an average number of divisors of quadratic polynomials. Archiv der Mathematik, 106.3 , 247-256.
6. Mauduit, C. & Rivat, J. (2009) La somme des chiffres des carrés. Acta Mathematica, 203.1, 107-148.
7. Sándor, J. & Crstici, B. (2004) Handbook of Number Theory II. Kluwer Academic, Dordrecht (2004).
8. Sándor, J., Mitrinovic, D.S. & Crstici, B. (2006) Handbook of Number Theory I. Springer, Netherlands.