Related papers: Generalizations of amicable numbers
In this paper some new ways of generalizing perfect numbers are investigated, numerical results are presented and some conjectures are established.
In this article, we study the properties of $\psi$-amicable numbers. We prove that their asymptotic density relative to the positive integers is zero. We also propose generalizations of $\psi$-amicable numbers.
This is an English translation of Euler's 1750 paper "De numeris amicabilibus" (E152), the most substantial of his three works with this name. In it, he expounds at great length the ad hoc methods he has developed to search for pairs of…
In this paper, we introduce new generalizations of higher-order Changhee of the first and second kind. Moreover, we derive some new results for these numbers and polynomials. Furthermore, some interesting special cases of the generalized…
In the present article, real number representations, that are generalizations of classical positive and alternating representations of numbers, are introduced and investigated. The main metric relation, properties of cylinder sets are…
The aim of the present article is to explore the possibilities of representing positive integers as sums of other positive integers and highlight certain fundamental connections between their multiplicative and additive properties. In…
In this paper, we introduce a generalization of Balancing and Balancing-Lucas numbers. We describe some of their properties also we give the related matrix representation and divisibility properties.
Numerous results on self-reciprocal polynomials over finite fields have been studied. In this paper we generalize some of these to a-self reciprocal polynomials defined in [4]. We consider some properties of the divisibility of a-reciprocal…
In this paper, we introduce a novel identity for generalized Euler polynomials, leading to further generalizations for several relations involving classical Euler numbers, Euler polynomials, Genocchi polynomials, and Genocchi numbers.
Two numbers $m$ and $n$ are considered amicable if the sum of their proper divisors, $s(n)$ and $s(m)$, satisfy $s(n) = m$ and $s(m) = n$. In 1981, Pomerance showed that the sum of the reciprocals of all such numbers, $P$, is a constant. We…
A new understanding of the notion of regularizer is proposed. It is argued that this new notion is more realistic than the old one and better fits the practical computational needs. An example of the regularizer in the new sense is given. A…
We introduce many new generalizations of Poisson algebras which can be constructed inside the associative algebra of linear transformations over a vector space.
We fix a gap in the proof of a result in our earlier paper "Generalised notions of amenability, II" (J. Funct. Anal. 254 (2008) 1776-1810), and so provide a new proof to a characterization of amenability for Beurling algebras. The result…
In this paper the concepts of character contractibility, approximate character amenability (contractibility) and uniform approximate character amenability (contractibility) are introduced. We are concerned with the relations among the…
We introduce a series of numbers which serve as a generalization of Bernoulli, Euler numbers and binomial coefficients. Their properties are applied to solve a probability problem and suggest a statistical test for independence and…
In this paper we introduce generalised Markov numbers and extend the classical Markov theory for the discrete Markov spectrum to the case of generalised Markov numbers. In particular we show recursive properties for these numbers and find…
In this paper, we present a new approach to the convolved Fibonacci numbers arising from the generating function of them and give some new and explicit identities for the convolved Fibonacci numbers.
A generalization of a distribution increases the flexibility particularly in studying of a phenomenon and its properties. Many generalizations of continuous univariate distributions are available in literature. In this study, an…
This is a short survey of amenable equivalence relations.
This research explores the sum of divisors - $\sigma(n)$ - and the abundancy index given by the function $\frac{\sigma(n)}{n}$. We give a generalization of amicable pairs - feebly amicable pairs (also known as harmonious pairs), that is…