Results 121 to 130 of about 41,624 (236)

On characterizing potential friends of 20

Annals of the West University of Timisoara: Mathematics and Computer Science
Does 20 have a friend? Or is it a solitary number? A folklore conjecture asserts that 20 has no friends, i.e., it is a solitary number. In this article, we prove that a friend N of 20 is of the form N = 2 · 52a ·m2, with (3;m) = (7;m) = 1 and it has at ...
Chatterjee Tapas, Mandal Sagar, Mandal Sourav   +2 more
doaj   +1 more source

Sums of three positive cubes

Journal of the London Mathematical Society, Volume 113, Issue 5, May 2026.
Abstract We survey ideas surrounding the study of the number of integers that can be represented as the sum of three positive cubes. We focus on the early contribution of Davenport using elementary techniques, and the subsequent developments due to Vaughan, which introduced Fourier analysis and mirrored many of the important developments of the Hardy ...
James Maynard
wiley   +1 more source

On Minkowski decomposition of Okounkov bodies on a Del Pezzo surface

Annales Universitatis Paedagogicae Cracoviensis: Studia Mathematica, 2011
We show that on a blow up of $P^2$ in $3$ general points there exists a finite set of nef divisors $P_1,ldots,P_s$ such that the Okounkov body $Delta(D)$ of an arbitrary effective $R$--divisor $D$ on $X$ is the Minkowski sum Delta(D)=sum_{i=1}
Patrycja Łuszcz-Świdecka
doaj  

Convolution Sums of Some Functions on Divisors

Rocky Mountain Journal of Mathematics, 2007
This is an old paper uploaded for archival ...
openaire   +4 more sources

A note on twin practical numbers

Le Matematiche, 2002
A positive integer m is a practical number if every positive integer n < m is a sum of distinct divisors of m. Let P_2 (x) be the counting function of the pairs (m, m + 2) of twin practical numbers. Margenstern gave a conjecture on P_2 (x).
Giuseppe Melfi
doaj  

MacMahon's sums-of-divisors and allied q-series

Advances in Mathematics
Here we investigate the $q$-series \begin{align*} \mathcal{U}_a(q)&=\sum_{n=0}^{\infty} MO(a;n)q^n&:=\sum_{0< ...
Amdeberhan, Tewodros, Ono, Ken, Singh, Ajit   +2 more
openaire   +2 more sources

Sum-avoiding sets in groups

Discrete Analysis, 2016
Sum-avoiding sets in groups, Discrete Analysis 2016:15, 27 pp. Let $A$ be a subset of an Abelian group $G$. A subset $B\subset A$ is called _sum-avoiding in $A$_ if no two elements of $B$ add up to an element of $A$.
Terence Tao, Van Vu
doaj   +1 more source

Sums of Proper Divisors with Missing Digits

Let $s(n)$ denote the sum of proper divisors of an integer $n$. In 1992, Erdős, Granville, Pomerance, and Spiro (EGPS) conjectured that if $\mathcal{A}$ is a set of integers with asymptotic density zero then $s^{-1}(\mathcal{A})$ also has asymptotic density zero.
Benli, K., Cesana, G., Dartyge, C., Dombrowsky, C., Thompson, L.   +4 more
openaire   +3 more sources

On some geometric properties of sequence spaces of generalized arithmetic divisor sum function

Journal of Inequalities and Applications
Recently, some new sequence spaces ℓ p ( A α ) $\ell _{p}(\mathfrak{A}^{\alpha })$ ( 0 < p < ∞ ) $(0 ...
Mohammad Mursaleen, Elvina Herawati
doaj   +1 more source

A note on generating identities for multiplicative arithmetic functions [PDF]

Contributions to Mathematics
Karol Gryszka
doaj   +1 more source