Arithmetic Properties Modulo Powers of 2 and 3 for Overpartition k-Tuples with Odd Parts

Abstract

Recently, Drema and N. Saikia (2023) and M. P. Saikia, Sarma, and Sellers (2025) proved several congruences modulo powers of 2 for overpartition triples with odd parts. In this paper we study further divisibility properties of overpartition k-tuples with odd parts using elementary means as well as properties of modular forms. In particular, we prove several congruences modulo multiples of 3, and an infinite family of congruences modulo powers of 3we also prove some cases of a conjecture of Saikia, Sarma, and Sellers. © Malaysian Mathematical Sciences Society and Penerbit Universiti Sains Malaysia 2026.