Results 31 to 40 of about 41,624 (236)

ON A PROBLEM OF PONGSRIIAM ON THE SUM OF DIVISORS [PDF]

Bulletin of the Australian Mathematical Society
For any positive integer n, let $\sigma (n)$ be the sum of all positive divisors of n. We prove that for every integer k with $1\leq k\leq 29$ and $(k,30)=1,$
Rui-Jing Wang
semanticscholar   +1 more source

Inequalities between some arithmetic functions, II [PDF]

Notes on Number Theory and Discrete Mathematics
As a continuation of Part I (see [1]), we offer new inequalities for classical arithmetic functions such as the Euler's totient function, the Dedekind's psi function, the sum of the positive divisors function, the number of divisors function, extended ...
Krassimir Atanassov, József Sándor, Mladen Vassilev-Missana   +2 more
doaj   +1 more source

Determination of the biquaternion divisors of zero, including the idempotents and nilpotents [PDF]

, 2008
The biquaternion (complexified quaternion) algebra contains idempotents (elements whose square remains unchanged) and nilpotents (elements whose square vanishes). It also contains divisors of zero (elements with vanishing norm).
Alfsmann, Daniel, Sangwine, Stephen J.
core   +2 more sources

On divisors of sums of integers. III [PDF]

Pacific Journal of Mathematics, 1988
The authors show that if \(\mathcal A_1, \ldots, \mathcal A_k\) are dense sets of integers then there is a sum \(a_1+\ldots+a_k\) with \(a_i\in\mathcal A_i\) that is divisible by a small prime. The prime factors of sums of integers are studied in a series of papers, especially a result of the above kind is implicit in \textit{A.
Pomerance, Carl, Sárközy, A., Stewart, C. L.   +2 more
openaire   +2 more sources

Power Values of Divisor Sums [PDF]

The American Mathematical Monthly, 2012
We consider positive integers whose sum of divisors is a perfect power. This problem had already caught the interest of mathematicians from the 17th century like Fermat, Wallis and Frenicle. In this article we study this problem and some variations.We also give an example of a cube, larger than one, whose sum of divisors is again a cube.
Beukers, F., Luca, Florian, Oort, F.
openaire   +3 more sources

Combinatorics of tropical Hurwitz cycles [PDF]

, 2015
We study properties of the tropical double Hurwitz loci defined by Bertram, Cavalieri and Markwig. We show that all such loci are connected in codimension one.
Hampe, Simon
core   +1 more source

Thirty-nine perfect numbers and their divisors

International Journal of Mathematics and Mathematical Sciences, 1986
The following results concerning even perfect numbers and their divisors are proved: (1) A positive integer n of the form 2p−1(2p−1), where 2p−1 is prime, is a perfect number; (2) every even perfect number is a triangular number; (3) τ(n)=2p, where τ(n ...
Syed Asadulla
doaj   +1 more source

Modular anomaly equation for Schur index of N $$ \mathcal{N} $$ = 4 super-Yang-Mills

Journal of High Energy Physics, 2022
We propose a novel modular anomaly equation for the unflavored Schur index in the N $$ \mathcal{N} $$ = 4 SU(N) super-Yang-Mills theory. The vanishing conditions overdetermine the modular ambiguity ansatz from the equation, thus together they are ...
Min-xin Huang
doaj   +1 more source

Extremal orders of some functions connected to regular integers modulo n

Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2013
Let V (n) denote the number of positive regular integers (mod n) less than or equal to n. We give extremal orders of , , , , where σ(n), ψ(n) are the sum-of-divisors function and the Dedekind function, respectively. We also give extremal orders for and ,
Brăduţ Apostol
doaj   +1 more source

Some new arithmetic functions [PDF]

Notes on Number Theory and Discrete Mathematics
We introduce and study some new arithmetic functions, connected with the classical functions φ (Euler's totient), ψ (Dedekind's function) and σ (sum of divisors function).
József Sándor, Krassimir Atanassov
doaj   +1 more source