Add to ORKGHere, we show, unconditionally for k = 3, and on the prime k-tuples conjecture for k ≥ 4, that n=1 σk(n) n! is irrational, where σk(n) denotes the sum of the kth powers of the divisors of n. 1
In 1978, Apéry [2] proved the irrationality of ζ(3) by constructing two explicit sequences of integ...
Abstract In this paper we prove some general results which imply, for example, the irrationality of ...
International audienceThis paper presents a complete formal verification of a proof that the evaluat...
For positive integers $k$ and $n$ let $\sigma_k(n)$ denote the sum of the $k$th powers of the diviso...
Denote by sigma(k)(n) the sum of the k-th powers of the divisors of n, and let S-k = Sigma(n >= 1) (...
AbstractLet σk(n) denote the sum of the k-th powers of the positive divisors of n. Erdős and Kac con...
AbstractLet ξ be a real irrational number, and φ be a function (satisfying some assumptions). In thi...
AbstractIn this paper we give irrationality results for numbers of the form ∑n=1∞ann! where the numb...
This is a preprint of an article published in Manuscripta Mathmatica (2005), Volume 117, Number 2, 1...
AbstractIn 1979 R. Apéry introduced the numbers an = Σ0n(kn)2(kn+k)2 in his irrationality proof for ...
1. Let Sen) be the Smarandache function. In paper [1] it is proved the irrationality of i S(7). We n...
The thesis deals with the irrationality, irrational sequences, linearly independent sums of series a...
AbstractThe function f(θ, φ; x, y) = Σk = 1∞ Σ1 ≤ m ≤ kθ + φ xkym, where θ > 0 is irrational and φ i...
AbstractApéry introduced a recurrence relation for a proof of the irrationality of ζ(3). Let an (n ≥...
In this paper we prove that all Smarandache concatenated k-power decimals are irrational numbers
In 1978, Apéry [2] proved the irrationality of ζ(3) by constructing two explicit sequences of integ...
Abstract In this paper we prove some general results which imply, for example, the irrationality of ...
International audienceThis paper presents a complete formal verification of a proof that the evaluat...
For positive integers $k$ and $n$ let $\sigma_k(n)$ denote the sum of the $k$th powers of the diviso...
Denote by sigma(k)(n) the sum of the k-th powers of the divisors of n, and let S-k = Sigma(n >= 1) (...
AbstractLet σk(n) denote the sum of the k-th powers of the positive divisors of n. Erdős and Kac con...
AbstractLet ξ be a real irrational number, and φ be a function (satisfying some assumptions). In thi...
AbstractIn this paper we give irrationality results for numbers of the form ∑n=1∞ann! where the numb...
This is a preprint of an article published in Manuscripta Mathmatica (2005), Volume 117, Number 2, 1...
AbstractIn 1979 R. Apéry introduced the numbers an = Σ0n(kn)2(kn+k)2 in his irrationality proof for ...
1. Let Sen) be the Smarandache function. In paper [1] it is proved the irrationality of i S(7). We n...
The thesis deals with the irrationality, irrational sequences, linearly independent sums of series a...
AbstractThe function f(θ, φ; x, y) = Σk = 1∞ Σ1 ≤ m ≤ kθ + φ xkym, where θ > 0 is irrational and φ i...
AbstractApéry introduced a recurrence relation for a proof of the irrationality of ζ(3). Let an (n ≥...
In this paper we prove that all Smarandache concatenated k-power decimals are irrational numbers
In 1978, Apéry [2] proved the irrationality of ζ(3) by constructing two explicit sequences of integ...
Abstract In this paper we prove some general results which imply, for example, the irrationality of ...
International audienceThis paper presents a complete formal verification of a proof that the evaluat...