Thirty-nine perfect numbers and their divisors.
Topological aspects of infinitude of primes in arithmetic progressions
We investigate properties of coset topologies on commutative domains with an identity, in particular, the 𝓢-coprime topologies defined by Marko and Porubský (2012) and akin to the topology defined by Furstenberg (1955) in his proof of the infinitude of rational primes. We extend results about the infinitude of prime or maximal ideals related to the Dirichlet theorem on the infinitude of primes from Knopfmacher and Porubský (1997), and correct some results from that paper. Then we determine cluster...
Triangular numbers whose sum of divisors is also triangular
Truncations of the ring of number-theoretic functions.
Two arithmetic functions and asymptotic densities of related sets
Two problems related to the non-vanishing of
We study two rather different problems, one arising from Diophantine geometry and one arising from Fourier analysis, which lead to very similar questions, namely to the study of the ranks of matrices with entries either zero or , where denotes the “centered” fractional part of . These ranks, in turn, are closely connected with the non-vanishing of the Dirichlet -functions at .