Values of arithmetical functions equal to a sum of two squares

William D. Banks; Florian Luca; Filip Saidak; Igor E. Shparlinski

doi:10.1093/qmath/hah039

Values of arithmetical functions equal to a sum of two squares

William D. Banks^*, Florian Luca, Filip Saidak, Igor E. Shparlinski

^*Corresponding author for this work

School of Computing

Research output: Contribution to journal › Article › peer-review

5 Citations (Scopus)

Abstract

Let φ(n) denote the Euler function. In this paper, we determine the order of growth for the number of positive integers n ≤ x for which φ(n) is the sum of two square numbers. We also obtain similar results for the Dedekind function ψ(n) and the sum of divisors function σ(n).

Original language	English
Pages (from-to)	123-139
Number of pages	17
Journal	Quarterly Journal of Mathematics
Volume	56
Issue number	2
DOIs	https://doi.org/10.1093/qmath/hah039
Publication status	Published - 2005

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title = "Values of arithmetical functions equal to a sum of two squares",

abstract = "Let φ(n) denote the Euler function. In this paper, we determine the order of growth for the number of positive integers n ≤ x for which φ(n) is the sum of two square numbers. We also obtain similar results for the Dedekind function ψ(n) and the sum of divisors function σ(n).",

author = "Banks, {William D.} and Florian Luca and Filip Saidak and Shparlinski, {Igor E.}",

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AU - Banks, William D.

AU - Luca, Florian

AU - Saidak, Filip

AU - Shparlinski, Igor E.

PY - 2005

Y1 - 2005

N2 - Let φ(n) denote the Euler function. In this paper, we determine the order of growth for the number of positive integers n ≤ x for which φ(n) is the sum of two square numbers. We also obtain similar results for the Dedekind function ψ(n) and the sum of divisors function σ(n).

AB - Let φ(n) denote the Euler function. In this paper, we determine the order of growth for the number of positive integers n ≤ x for which φ(n) is the sum of two square numbers. We also obtain similar results for the Dedekind function ψ(n) and the sum of divisors function σ(n).

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U2 - 10.1093/qmath/hah039

DO - 10.1093/qmath/hah039

M3 - Article

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SP - 123

EP - 139

JO - Quarterly Journal of Mathematics

JF - Quarterly Journal of Mathematics

SN - 0033-5606

IS - 2

ER -

Values of arithmetical functions equal to a sum of two squares

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