2 papers
math.NT2025
Arithmetic properties of MacMahon-type sums of divisors: the odd case
James A. Sellers, Roberto Tauraso
A century ago, P. A. MacMahon introduced two families of generating functions, $$ \sum_{1\leq n_1<n_2<\cdots<n_t}\prod_{k=1}^t\frac{q^{n_k}}{(1-q^{n_k})^2} \quad\text{ and } \sum_{…
math.NT2025
Arithmetic properties of MacMahon-type sums of divisors
James A. Sellers, Roberto Tauraso
In this paper, we prove several new infinite families of Ramanujan--like congruences satisfied by the coefficients of the generating function which is an extension of Ma…