MMN-2470

# Certain combinatoric convolution sums arising from Bernoulli and Euler Polynomials

**Daeyeoul Kim**, Department of Mathematics and Institute of Pure and Applied Mathematics, Chon-buk National University,`kdaeyeoul@jbnu.ac.kr`

**Umit Sarp**, Department of Mathematics, Balikesir University,`umitsarp@ymail.com`

**Sebahattin Ikikardes**, Department of Mathematics, Balikesir University,`skardes@balikesir.edu.tr`

## Abstract

In this study, we introduce the absolute M\"obius divisor function $U\left( n \right)$. Also we investigate the sequences ${{\left( {{U}_{m}}\left( n \right) \right)}_{m}}$, which concerns the iteration of the absolute M\"obius divisor function $U\left(n\right)$. According to some numerical computational evidence, we consider integer pairs (n; n + 1) satisfying;
$\varphi \left( n \right)=\varphi \left( n+1 \right)=U\left( n \right)=U\left( n+1 \right).$
Furthermore, we give some examples and proofs for our results.

Vol. 20 (2019), No. 1, pp. 311-330

DOI: 10.18514/MMN.2019.2470