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Arithmetic properties of MacMahon-type sums of divisors

2024/11/18 by James A. Sellers, Sellers, James A., Roberto Tauraso +1 · 2 citations
Mathematics · #Analytic Number Theory Research #History and Theory of Mathematics

paper · pdf · doi:10.48550/arxiv.2411.11404

Abstract

In this paper, we prove several new infinite families of Ramanujan--like congruences satisfied by the coefficients of the generating function Ut(a,q) which is an extension of MacMahon's generalized sum-of-divisors function. As a by-product, we also show that, for all n≥ 0, B3(15n+7)≡ 0 \pmod5 where B3(n) is the number of almost 3-regular overpartitions of n.

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