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M. Merca. Combinatorial interpretations of a recent convolution for the number of divisors of a positive integer. Journal of Number Theory, 160, pp. 60-75, 2016.

Abstract: In this paper, we give a refined form of a recent factorization of Lambert series. This result allows us to prove new connections between partitions and divisors of positive integers, such as a new formula for the number of divisors of a positive integer as a convolution. Three recurrence relations for computing the number of partitions of a positive integer into distinct parts are rediscovered in this context.

Keywords: Divisors, Lambert series, Partitions

URL: http://dx.doi.org/10.1016/j.jnt.2015.08.014

Posted by Mircea Merca

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