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Pairs of square-free values of the type $n^{2} + 1$ , $n^{2} + 2$

Stoyan Dimitrov (2021)

Czechoslovak Mathematical Journal

We show that there exist infinitely many consecutive square-free numbers of the form $n^{2} + 1$ , $n^{2} + 2$ . We also establish an asymptotic formula for the number of such square-free pairs when $n$ does not exceed given sufficiently large positive number.

Permanence de relations de récurrence dans certains développements asymptotiques. (Permanence of recurrence relations in certain asymptotic expansions).

Robin, Guy (1988)

Publications de l'Institut Mathématique. Nouvelle Série

Polylogarithms and arithmetic function spaces

Lutz G. Lucht, Anke Schmalmack (2000)

Acta Arithmetica

Positive integers $n$ such that $n ∣ a^{σ (n)} - 1$ .

Luca, Florian (2003)

Novi Sad Journal of Mathematics

Positive integers $n$ such that $σ (ϕ (n)) = σ (n)$ .

De Koninck, Jean-Marie, Luca, Florian (2008)

Journal of Integer Sequences [electronic only]

Power Series with Multiplicative Coefficients.

Lutz Lucht (1981)

Mathematische Zeitschrift

Pretentiousness in analytic number theory

Andrew Granville (2009)

Journal de Théorie des Nombres de Bordeaux

In this report, prepared specially for the program of the XXVième Journées Arithmétiques, we describe how, in joint work with K. Soundararajan and Antal Balog, we have developed the notion of “pretentiousness” to help us better understand several key questions in analytic number theory.