Related papers: Generalizations of amicable numbers
We develop new closed form representations of sums of (n + {\alpha})th shifted harmonic numbers and reciprocal binomial coefficients in terms of {\alpha}th shifted harmonic numbers. Some interesting new consequences and illustrative…
In this paper we discuss generalized group, provides some interesting examples. Further we introduce a generalized module as a module like structure obtained from a generalized group and discuss some of its properties and we also describes…
We introduce a new type of means. It is new in two ways: its domain consists of sets and its values are sets too. We investigate the properties and behavior of such generalization. We also present many naturally arisen examples for such…
This paper gives new explicit formulas for sums of powers of integers and their reciprocals.
In this paper, we consider infinite sums derived from the reciprocals of the generalized Fibonacci numbers. We obtain some new and interesting identities for the generalized Fibonacci numbers.
In this paper we introduce the generalization of Multi Poly-Euler polynomials and we investigate some relationship involving Multi Poly-Euler polynomials. Obtaining a closed formula for generalization of Multi Poly-Euler numbers therefore…
In two recent articles we have examined a generalization of the binomial distribution associated with a sequence of positive numbers, involving asymmetric expressions of probabilities that break the symmetry {\it win-loss}. We present in…
In this paper, we give a new discovery of conversion of generalized singular values. New formulation is proposed.
This paper builds on the research initiated by Boyadzhiev, but introduces generalized harmonic numbers, \[ H_n(\alpha)= \sum_{k=1}^n \frac{\alpha^{k}}{k}, \] which enable the derivation of new identities as well as the reformulation of…
A new $q$-analogue of Appell polynomial sequences and their generalizations are introduced and their main characterizations are proved. As consequences new $q$-analogue of Bernoulli and Euler polynomials and numbers is introduced, their…
The aim of this paper is to extend the external characterization of I-favorable spaces. This allows us to obtain a characterization of compact I-favorable spaces in terms of quasi k-metrics. We also provide proofs of some author's results…
In this paper we present many congruences for several Ap\'ery-like sequences.
In the present paper we generalize the Eulerian numbers (also of the second and third orders). The generalization is connected with an autonomous first-order differential equation, solutions of which are used to obtain integral…
In the paper, we generalize some congruences of Lehmer for general composite numbers.
We give a survey of some known and some new results about factors of different sorts of $q-$Fibonacci numbers.
The aim of this paper is to introduce Bell polynomials and numbers of the second kind and poly-Bell polynomials and numbers of the second kind, and to derive their explicit expressions, recurrence relations and some identities involving…
In this paper, we will define general Eulerian numbers and Eulerian polynomials based on general arithmetic progressions. Under the new definitions, we have been successful in extending several well-known properties of traditional Eulerian…
In this paper, we derive some interesting symmetric properties for the geenralized Euler numbers and polynomials.
This paper presents a formalization of the theory of amicable numbers in the Lean~4 proof assistant. Two positive integers $m$ and $n$ are called an amicable pair if the sum of proper divisors of $m$ equals $n$ and the sum of proper…
The article is devoted to introduce and investigation of new numeral systems. These representations are generalizations of classical representations of real numbers. The main properties of investigating representations are described. The…