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Divisibility

  • Chapter
Unsolved Problems in Number Theory

Part of the book series: Problem Books in Mathematics ((1605,volume 1))

Abstract

We will denote by d(n) the number of positive divisors of n, by σ(n) the sum of those divisors, and by σ k (n) the sum of their kth powers, so that σ0(n) = d(n) and σ1(n)= σ(n). We use s(n) for the sum of the aliquot parts of n, i.e., the positive divisors of n other than n itself, so that s(n) = σ(n)—n. The number of distinct prime factors of n will be denoted by ω(n) and the total number, counting repetitions, by Ω(n).

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  1. Department of Mathematics and Statistics, The University of Calgary, Calgary, Alberta, T2N 1N4, Canada

    Richard K. Guy

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© 1994 Springer Science+Business Media New York

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Guy, R.K. (1994). Divisibility. In: Unsolved Problems in Number Theory. Problem Books in Mathematics, vol 1. Springer, New York, NY. https://doi.org/10.1007/978-1-4899-3585-4_3

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  • DOI: https://doi.org/10.1007/978-1-4899-3585-4_3

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