Results 11 to 20 of about 381,379 (275)

On an additive arithmetic function [PDF]

Pacific Journal of Mathematics, 1977
Let \(n\) be a positive integer, \(n=\prod\limits_{i=1}^rp_i^{\alpha_i}\) in canonical form, and let \(A(n)=\sum\limits_{i=1}^r\alpha_ip_i\). Clearly \(A\) is an additive arithmetic function.
Alladi, K., Erdős, P.
openaire   +2 more sources

On certain arithmetic functions involving the greatest common divisor

Open Mathematics, 2012
Krätzel Ekkehard, Nowak Werner, Tóth László   +2 more
doaj   +2 more sources

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

On certain bounds for the divisor function [PDF]

Notes on Number Theory and Discrete Mathematics
We offer various bounds for the divisor function d(n), in terms of n, or other arithmetical functions.
József Sándor
doaj   +1 more source

Neural computation of arithmetic functions [PDF]

, 1990
A neuron is modeled as a linear threshold gate, and the network architecture considered is the layered feedforward network. It is shown how common arithmetic functions such as multiplication and sorting can be efficiently computed in a shallow neural ...
Bruck, Jehoshua, Siu, Kai-Yeung
core   +1 more source

On certain arithmetical products involving the divisors of an integer [PDF]

Notes on Number Theory and Discrete Mathematics
We study the arithmetical products Π d^d, Πd^{1/d} and Πd^{log d}, where d runs through the divisors of an integer n>1.
József Sándor
doaj   +1 more source

The arithmetic derivative and Leibniz-additive functions [PDF]

, 2018
An arithmetic function $f$ is Leibniz-additive if there is a completely multiplicative function $h_f$, i.e., $h_f(1)=1$ and $h_f(mn)=h_f(m)h_f(n)$ for all positive integers $m$ and $n$, satisfying $$ f(mn)=f(m)h_f(n)+f(n)h_f(m) $$ for all positive ...
Haukkanen, Pentti, Merikoski, Jorma K., Tossavainen, Timo   +2 more
core   +3 more sources

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

Arithmetic functions at consecutive shifted primes [PDF]

, 2014
For each of the functions $f \in \{\phi, \sigma, \omega, \tau\}$ and every natural number $k$, we show that there are infinitely many solutions to the inequalities $f(p_n-1) < f(p_{n+1}-1) < \dots < f(p_{n+k}-1)$, and similarly for $f(p_n-1) > f(p_{n+1 ...
Pollack, Paul, Thompson, Lola
core   +2 more sources

On certain inequalities for φ, ψ, σ and related functions, III [PDF]

Notes on Number Theory and Discrete Mathematics
We obtain generalizations of certain results from [2] and [4]. The unitary variants are also considered. Some new arithmetic functions and their inequalities are also considered.
József Sándor, Karol Gryszka
doaj   +1 more source