Divisibility of sums of some restricted partition numbers by \(2, 3\) and \(4\) (Q6564832)

In 2017, \textit{C. Ballantine} and \textit{M. Merca} [Ramanujan J. 44, No. 3, 617--630 (2017; Zbl 1379.05004)] explored the parity of sums of partition numbers at certain places in arithmetic progressions. Recently, \textit{N. D. Baruah} [``Divisibiliy of sums of partition numbers by multiples of 2 and 3'', Bull. Aust. Math. Soc. (to appear)] offered some results on divisibility by multiples of \(2\) and \(3\) of sums of partition numbers which do not rely on the squares in arithmetic progressions. In this paper, the authors study divisibility by \(2\), \(3\) and \(4\) of sums of partition numbers into distinct odd parts, sums of \(2\)-core partition numbers and sums of partition numbers into odd parts.