Journal of Integer Sequences, Vol. 17 (2014), Article 14.9.8

Another Proof of a Conjecture by Hirschhorn and Sellers on Overpartitions

Liuquan Wang
Department of Mathematics
National University of Singapore
Singapore, 119076


We provide a new elementary proof for a Ramanujan-type congruence for the overpartition function modulo 40, which was previously conjectured by Hirschhorn and Sellers and later proved by Chen and Xia. We also find some new congruences for the overpartition function modulo 5 and 9.

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(Concerned with sequence A015128.)

Received July 24 2014; revised versions received August 25 2014; September 5 2014. Published in Journal of Integer Sequences, September 7 2014.

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