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On the average value of the least common multiple of k positive integers

Hilberdink, T. and Tóth, L. (2016) On the average value of the least common multiple of k positive integers. Journal of Number Theory, 169. pp. 327-341. ISSN 0022-314X

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To link to this item DOI: 10.1016/j.jnt.2016.05.024


We deduce an asymptotic formula with error term for the sum ∑n1,…,nk≤xf([n1,…,nk]), where [n1,…,nk] stands for the least common multiple of the positive integers n1,…,nk (k≥2) and f belongs to a large class of multiplicative arithmetic functions, including, among others, the functions f(n)=nr, φ(n)r, σ(n)r (r>−1 real), where φ is Euler's totient function and σ is the sum-of-divisors function. The proof is by elementary arguments, using the extension of the convolution method for arithmetic functions of several variables, starting with the observation that given a multiplicative function f, the function of k variables f([n1,…,nk]) is multiplicative.

Item Type:Article
Divisions:Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics
ID Code:66057


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