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2 results

  • WEAK PROPER DISTRIBUTION OF VALUES OF MULTIPLICATIVE FUNCTIONS IN RESIDUE CLASSES

  • Part of
  • WŁADYSŁAW NARKIEWICZ
  • Journal:
    Journal of the Australian Mathematical Society / Volume 93 / Issue 1-2 / October 2012
    Published online by Cambridge University Press:
    04 February 2013, pp. 173-188
    Print publication:
    October 2012
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  • For a class of multiplicative integer-valued functions $f$ the distribution of the sequence $f(n)$ in restricted residue classes modulo $N$ is studied. We consider a property weaker than weak uniform distribution and study it for polynomial-like multiplicative functions, in particular for $\varphi (n)$ and $\sigma (n)$.

  • WHEN THE SUM OF ALIQUOTS DIVIDES THE TOTIENT

  • William D. Banks, Florian Luca
  • Journal:
    Proceedings of the Edinburgh Mathematical Society / Volume 50 / Issue 3 / October 2007
    Published online by Cambridge University Press:
    08 January 2008, pp. 563-569
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  • Let $\varphi(\cdot)$ be the Euler function and let $\sigma(\cdot)$ be the sum-of-divisors function. In this note, we bound the number of positive integers $n\le x$ with the property that $s(n)=\sigma(n)-n$ divides $\varphi(n)$.