arXiv subjects
Publications and source records attributed to Antal Bege.
Let $f$ be an arithmetical function. The matrix $[f[i,j]]_{n\times n}$ given by the value of $f$ in least common multiple of $[i,j]$, $f\big([i,j]\big)$ as its $i,\; j$ entry is called the least common multiple (LCM) matrix. We consider the generalization of this matrix where the elements are in the form $f\big(n,[i,j]\big)$ and $f\big(n,i,j,[i,j]\big)$.
Let $f$ be an arithmetical function. The matrix $[f(i,j)]_{n\times n}$ given by the value of $f$ in greatest common divisor of $(i,j)$, $f\big((i,j)\big)$ as its $i,\; j$ entry is called the greatest common divisor (GCD) matrix. We consider the generalization of this matrix where the elements are in the form $f\big(i,(i,j)\big)$.
In this paper some new ways of generalizing perfect numbers are investigated, numerical results are presented and some conjectures are established.
A coding method using binary sequences is presented for different computation problems related to Catalan numbers. This method proves in a very easy way the equivalence of these problems.
In [3] Bege introduced the generalized Apostol's Mobius functions. In this paper we are presenting new properties of this functions. By introducing the special set of k-free numbers we have obtained some asymptotic formulas for the partial sums of these functions.
Apostol's Mobius functions of order k are generalized to depend on a second integer parameter m. Asymptotic formulas are obtained for the partial sums of these generalized functions.