Certain combinatoric convolution sums arising from Bernoulli and Euler Polynomials

摘要

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