Arithmetic properties of the DSOME function

Recently, Andrews and Ghosh Dastidar [Ramanujan J. 69 (2026), art. 26] studied two interesting functions SOME(n) and DSOME(n), where SOME(n) is the sum of all the odd parts in the partitions of n minus the sum of all the even parts, and DSOME(n) is the sum of all the odd parts in the partitions of n into distinct parts minus the sum of all the even parts. They expressed the generating functions of SOME(n) and DSOME(n) in terms of q-series and found several interesting congruences modulo 4 and 5. In this paper, we express the generating function of DSOME(n) in closed form, which allows us to find some new congruences and internal congruences modulo 4 and 8 for DSOME(n).