Results 201 to 210 of about 41,624 (236)

Sums of higher divisor functions

Journal of Number Theory, 2021
The authors study the average behavior of the $k$th divisor (or Piltz divisor) function over values of the quadratic form $(n_1)^2+\dots+ (n_l)^2$ with $l>=3$. For $k=2$ and $l=3$ an earlier result is due to [\textit{L. Zhao}, Acta Arith. 163, No. 2, 161--177 (2014; Zbl 1346.11056)], while for $k=3$, $l=3$ to [\textit{Q. Sun} and \textit{D.
Hu, Guangwei, Lü, Guangshi
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An Ω-theorem for an error term related to the sum-of-divisors function

Monatshefte Fur Mathematik, 1987
Y. Pétermann
semanticscholar   +3 more sources

Sums of the Divisor Function

Canadian Journal of Mathematics, 1964
Shapiro and Warga (2) have proved in an elementary way that all large integers are expressible as the sum of at most 20 primes. In so doing, they proved thatas x —> ∞, where u is a positive square-free integer,
Gordon, B., Rogers, K.
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ON THE SUMS OF COMPLEMENTARY DIVISORS

International Journal of Number Theory, 2007
In this paper, we study various arithmetic properties of d + n/d, where d runs through all the τ(n) positive divisors of n. For example, denoting by ϖ(n) the number of prime values among these sums, we study how often ϖ(n) > 0 and also ϖ(n) = τ(n), and we also evaluate the average value of ϖ(n).
Becheanu, Mircea, Luca, Florian, Shparlinski, Igor E.   +2 more
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Divisor Sums of Generalised Exponential Polynomials

Canadian Mathematical Bulletin, 1996
AbstractA study is made of sums of reciprocal norms of integral and prime ideal divisors of algebraic integer values of a generalised exponential polynomial. This includes the important special cases of linear recurrence sequences and general sums of S-units.
Everest, G. R., Shparlinski, I. E.
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Some Equations Concerning the Sum of Divisors Function

PUMP journal of undergraduate research
In this article, I wiil consider four equations involving the sum of divisors function, σ, and I will prove that for the first two there are infinitely many solutions, while for the other two I will provide some particular solutions.
Andreea Dima
semanticscholar   +1 more source

Mean Value Estimation of The Sum-of-divisors Function

Journal of Innovation and Development
 The sum-of-divisor function is one of the important number theory functions, and the study of the properties of the sum-of-divisor function can provide more methods for solving some number theory problems.
Wanchun Pu
semanticscholar   +1 more source

Sums of Divisors, Perfect Numbers and Factoring

SIAM Journal on Computing, 1984
Let \(N\) be a positive integer, and let \(\sigma(N)\) denote the sum of the divisors of \(N\). We show computing \(\sigma(N)\) is equivalent to factoring \(N\) in the following sense: there is a random polynomial time algorithm that, given \(\sigma(N)\), produces the prime factorization of \(N\), and \(\sigma(N)\) can be computed in polynomial time ...
Bach, Eric, Miller, Gary, Shallit, Jeffrey   +2 more
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Palindromic Sums of Proper Divisors

2015
See the abstract in the attached pdf.
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Sum of higher divisor function with prime summands

Czechoslovak Mathematical Journal, 2023
Let \(\tau_{k}(n)\) denote the \(k\)-th divisor function, counting the number of representations \(m_1\cdots m_k=n\) with \(1\leq m_1,\dots ,m_k\leq n\). Inspired by the recent work of \textit{G. Hu} and \textit{G. Lü} [J. Number Theory 220, 61--74 (2021; Zbl 1466.11065)], the authors obtain an asymptotic for the following sum running over primes \(p_1,
Ding, Yuchen, Zhou, Guang-Liang
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