Results 31 to 40 of about 654 (59)

The sum of the unitary divisor function [PDF]

, 2014
This article establishes a new upper bound on the function $\sigma^{*}(n)$, the sum of all coprime divisors of $n$. The article concludes with two questions concerning this function.Comment: 6 pages, to appear in Publ. Inst. Math. (Beograd) (N.S.
Trudgian, Tim
core  

Factorization of factorials and a result of Hardy and Ramanujan

, 2012
We obtain an explicit approximation for the sum of prime powers in the factorization of n! into prime numbers. This reproves, as more as gives an explicit version to, a well-known result of Hardy and Ramanujan concerning the summation ∑k n Ω(k ...
M. Hassani
semanticscholar   +1 more source

A note on bounds for norms of the reciprocal LCM matrix

, 2004
Let S = {x1, x2, . . . , xn} be a set of distinct positive integers and [xi, xj] denote the least common multiple of xi and xj . The matrix [S−1] = (sij) , where sij = 1 [xi,xj] , is called the reciprocal least common multiple (reciprocal LCM) matrix on ...
E. Altınışık, Naim Tuglu, P. Haukkanen   +2 more
semanticscholar   +1 more source

Binomial convolution sum of divisor functions associated with Dirichlet character modulo 8

Open Mathematics
In this article, we compute binomial convolution sums of divisor functions associated with the Dirichlet character modulo 8, which is the remaining primitive Dirichlet character modulo powers of 2 yet to be considered.
Jin Seokho, Park Ho
doaj   +1 more source

Some Generalizations for a Theorem by Landau

, 2001
Let π(x) be the number of primes not exceeding x . E. Landau made the following conjecture: π(2x) 2π(x) for integer x 2 . In 1966 Rosser and Schoenfeld proved this conjecture. In the present paper we establish upper bounds for π(x + y) .
L. Panaitopol
semanticscholar   +1 more source

On the matrix norms of a GCD related matrix

, 2008
In this paper we investigate the matrix norms of a GCD related matrix, i.e., (Sf ) = ( f (i, j)/(irjr) ) for multiplicative arithmetical functions f .
E. Altınışık
semanticscholar   +1 more source

A note on Deaconescu’s conjecture

Annals of the West University of Timisoara: Mathematics and Computer Science
Hasanalizade [5] studied Deaconescu’s conjecture for positive composite integer n. A positive composite integer n ≥ 4 is said to be a Deaconescu number if S2(n) | ϕ(n) − 1.
Mandal Sagar
doaj   +1 more source

Extreme values of the Dedekind $\Psi$ function

, 2011
Let $\Psi(n):=n\prod_{p | n}(1+\frac{1}{p})$ denote the Dedekind $\Psi$ function. Define, for $n\ge 3,$ the ratio $R(n):=\frac{\Psi(n)}{n\log\log n}.$ We prove unconditionally that $R(n)< e^\gamma$ for $n\ge 31.$ Let $N_n=2...p_n$ be the primorial of ...
Planat, Michel, Solé, Patrick
core   +1 more source

Computing sums in terms of beta, polygamma, and Gauss hypergeometric functions. [PDF]

Rev R Acad Cienc Exactas Fis Nat A Mat, 2020
Qi F, Huang CJ.
europepmc   +1 more source

On a question of A. Schinzel: Omega estimates for a special type of arithmetic functions

Open Mathematics, 2013
Kühleitner Manfred, Nowak Werner
doaj   +1 more source