Journal of Integer Sequences, Vol. 20 (2017), Article 17.4.3

Congruences Modulo Small Powers of 2 and 3 for Partitions into Odd Designated Summands

B. Hemanthkumar
Department of Mathematics
M. S. Ramaiah University of Applied Sciences
Bengaluru-560 058

H. S. Sumanth Bharadwaj and M. S. Mahadeva Naika
Department of Mathematics
Central College Campus
Bangalore University
Bengaluru-560 001


Andrews, Lewis and Lovejoy introduced a new class of partitions, partitions with designated summands. Let PD(n) denote the number of partitions of n with designated summands and PDO(n) denote the number of partitions of n with designated summands in which all parts are odd. Andrews et al. established many congruences modulo 3 for PDO(n) by using the theory of modular forms. Baruah and Ojah obtained numerous congruences modulo 3, 4, 8 and 16 for PDO(n) by using theta function identities. In this paper, we prove several infinite families of congruences modulo 9, 16 and 32 for PDO(n).

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(Concerned with sequences A077285 A102186.)

Received October 25 2016; revised version received January 13 2017; January 23 2017. Published in Journal of Integer Sequences, January 28 2017.

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