Abstract
We will denote by d(n) the number of positive divisors of n, by σ(n) the sum of those divisors, and by σk(n) the sum of their kth powers, so that σ 0(n) = d(n) and σ l(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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Guy, R.K. (2004). Divisibility. In: Unsolved Problems in Number Theory. Problem Books in Mathematics, vol 1. Springer, New York, NY. https://doi.org/10.1007/978-0-387-26677-0_3
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