Results 11 to 20 of about 56 (56)

Sequences and series involving the sequence of composite numbers

International Journal of Mathematics and Mathematical Sciences, Volume 31, Issue 1, Page 31-36, 2002., 2002
Denoting by pn and cn the nth prime number and the nth composite number, respectively, we prove that both the sequence (xn)n≥1, defined by xn=∑k=1n (ck+1−ck) / k−pn / n, and the series ∑n=1∞ (pcn−cpn) / npn are convergent.
Panayiotis Vlamos
wiley   +1 more source

Properties of the function f(x) = x/π(x)

International Journal of Mathematics and Mathematical Sciences, Volume 28, Issue 5, Page 307-311, 2001., 2001
We obtain the asymptotic estimations for ∑k=2nf(k) and ∑k=2n1/f(k), where f(k) = k/π(k), k ≥ 2. We study the expression 2f(x + y) − f(x) − f(y) for integers x, y ≥ 2 and as an application we make several remarks in connection with the conjecture of Hardy and Littlewood.
Panayiotis Vlamos
wiley   +1 more source

Some characterizations of totients

International Journal of Mathematics and Mathematical Sciences, Volume 19, Issue 2, Page 209-217, 1996., 1995
An arithmetical function is said to be a totient if it is the Dirichlet convolution between a completely multiplicative function and the inverse of a completely multiplicative function. Euler′s phi‐function is a famous example of a totient. All completely multiplicative functions are also totients.
Pentti Haukkanen
wiley   +1 more source

Harmonic numbers, harmonic series and zeta function

Moroccan Journal of Pure and Applied Analysis, 2018
This paper reviews, from different points of view, results on Bernoulli numbers and polynomials, the distribution of prime numbers in connexion with the Riemann hypothesis. We give an account on the theorem of G. Robin, as formulated by J. Lagarias.
Sebbar Ahmed
doaj   +1 more source

The unitary amicable pairs to 108

International Journal of Mathematics and Mathematical Sciences, Volume 18, Issue 2, Page 405-410, 1995., 1994
We present an exhaustive list of the 185 unitary amicable pairs whose smaller number is less than 108 and a new unitary sociable set of four numbers.
Rudolph M. Najar
wiley   +1 more source

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

An identity for a class of arithmetical functions of several variables

, 1993
International Journal of Mathematics and Mathematical Sciences, Volume 16, Issue 2, Page 355-358, 1993.
Pentti Haukkanen
wiley   +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

Dirichlet summations and products over primes

, 1991
International Journal of Mathematics and Mathematical Sciences, Volume 16, Issue 2, Page 359-372, 1993.
Geoffrey B. Campbell
wiley   +1 more source

Arithmetic functions associated with infinitary divisors of an integer

, 1993
International Journal of Mathematics and Mathematical Sciences, Volume 16, Issue 2, Page 373-383, 1993.
Graeme L. Cohen, Peter Hagis
wiley   +1 more source