Journal of Integer Sequences, Vol. 18 (2015), Article 15.2.8

On the Largest Product of Primes with Bounded Sum

Marc Deléglise and Jean-Louis Nicolas
Institut Camille Jordan
Université de Lyon, CNRS
F-69622 Villeurbanne Cedex


Let h(n) denote the largest product of primes whose sum is ≤ n, and g(n) denote the Landau function, which is the largest product of powers of primes whose sum is ≤ n. In this article, several properties of h(n) are given and compared to similar properties of g(n). Special attention is paid to the behavior of the largest prime factor of h(n).

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(Concerned with sequences A000793 A159685.)

Received September 22 2014; revised version received January 15 2015. Published in Journal of Integer Sequences, January 25 2015.

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