Journal of Integer Sequences, Vol. 25 (2022), Article 22.2.3

The Number of Prime Factors on Average in Certain Integer Sequences


Rafael Jakimczuk
División Matemática
Universidad Nacional de Luján
Buenos Aires
Argentina

Matilde Lalín
Département de mathématiques et de statistique
Université de Montréal
CP 6128, succ. Centre-ville
Montréal, QC H3C 3J7
Canada

Abstract:

Let Ω(n) denote the total number of primes in the factorization of the integer n. We obtain asymptotic formulae for the sums Σn ≤ x Ω(n), where n runs over the square-free numbers, the square-full numbers, the perfect powers, and generalizations of these families of numbers.

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(Concerned with sequences A001694 A004709 A005117 A036966.)

Received October 29 2021; revised versions received November 17 2021; January 17 2022. Published in Journal of Integer Sequences, January 30 2022.

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