Almost-even functions as solutions of a linear functional equation
Amicable Pell numbers.
An addendum to the paper: “Arithmetic functions over rings with zero divisors” by Ruangsinsap, Laohakosol and P. Udomkavanich.
An analogue in certain unique factorization domains of the Euclid-Euler theorem on perfect numbers.
An arithmetic formula of Liouville
An elementary proof is given of an arithmetic formula, which was stated but not proved by Liouville. An application of this formula yields a formula for the number of representations of a positive integer as the sum of twelve triangular numbers.
An arithmetic function
An arithmetical mapping and applications to Ω-results for the Riemann zeta function
An extension of Daykin's generalized Möbius function to unitary divisors.
An identity for a class of arithmetical functions of several variables.
An identity for a class of arithmetical functions of two variables.
An identity involving multiplicative orders.
An identity involving Ramanujan's sum.
An iteration problem involving the divisor function
An unconventional problem in the elementary theory of numbers
An upper bound for odd perfect numbers.
Analytic Eisenstein series, theta-functions, and series relations in the spirit of Ramanujan.
Application of the circle method on multidimensional limit-periodic functions
Applications of differential algebra to algebraic independence of arithmetic functions
We generalize and unify the proofs of several results on algebraic independence of arithmetic functions and Dirichlet series by using a theorem of Ax on the differential Schanuel conjecture. Along the way, we find counter-examples to some results in the literature.
Arithmetic functions and weighted averages
Arithmetic functions associated with the infinitary divisors of an integer.