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• # Artykuł - szczegóły

## Colloquium Mathematicum

2011 | 123 | 1 | 115-127

## On the distribution of the partial sum of Euler's totient function in residue classes

EN

### Abstrakty

EN
We investigate the distribution of $Φ(n) = 1+ ∑_{i=1}ⁿ φ(i)$ (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 C. Pomerance on the distribution of φ(n) modulo 3.

115-127

wydano
2011

### Twórcy

autor
• Department of Mathematics, University of Illinois at Urbana-Champaign, 1409 W. Green Street, Urbana, IL 61801, U.S.A.
autor
• Department of Mathematics, University of Illinois at Urbana-Champaign, 1409 W. Green Street, Urbana, IL 61801, U.S.A.
autor
• Department of Mathematics, University of Illinois at Urbana-Champaign, 1409 W. Green Street, Urbana, IL 61801, U.S.A.