Divisor problems in special sets of positive integers.
Nowak, W.G. (1992)
Acta Mathematica Universitatis Comenianae. New Series
J. Pintz (1977)
Acta Arithmetica
Štefan Porubský (1972)
Matematický časopis
Richard H. Hudson (1977)
Journal für die reine und angewandte Mathematik
Alan Zame (1972)
Colloquium Mathematicae
L. Hajdu, N. Saradha (2010)
Acta Arithmetica
R. Stoneham (1973)
Acta Arithmetica
Christopher Hooley (1967)
Journal für die reine und angewandte Mathematik
J. Friedlander (1973)
Acta Arithmetica
Adolf Hildebrand (1986)
Monatshefte für Mathematik
Angkana Sripayap, Pattira Ruengsinsub, Teerapat Srichan (2022)
Czechoslovak Mathematical Journal
Let and . Denote by the set of all integers whose canonical prime representation has all exponents
Amora Nongkynrih (1995)
Acta Arithmetica
Manfred Kühleitner (1996)
Commentationes Mathematicae Universitatis Carolinae
A certain generalized divisor function is studied which counts the number of factorizations of a natural number into integer powers with prescribed exponents under certain congruence restrictions. An -estimate is established for the remainder term in the asymptotic for its Dirichlet summatory function.
Wenpeng Zhang (2001)
Acta Arithmetica
Richard H. Hudson (1973)
Journal für die reine und angewandte Mathematik
Karl K. Norton (1972)
Journal für die reine und angewandte Mathematik
Cristian Cobeli, Alexandru Zaharescu (1998)
Acta Arithmetica
Youness Lamzouri, M. Tip Phaovibul, Alexandru Zaharescu (2011)
Colloquium Mathematicae
We investigate the distribution of (which counts the number of Farey fractions of order n) in residue classes. While numerical computations suggest that Φ(n) is equidistributed modulo q if q is odd, and is equidistributed modulo the odd residue classes modulo q when q is even, we prove that the set of integers n such that Φ(n) lies in these residue classes has a positive lower density when q = 3,4. We also provide a simple proof, based on the Selberg-Delange method, of a result of T. Dence and...
Müller, Tom (2010)
Journal of Integer Sequences [electronic only]
Yaming Lu, Yuan Yi (2010)
Acta Arithmetica