Journal of Integer Sequences, Vol. 19 (2016), Article 16.5.7

Arithmetic Properties of Partition k-tuples with Odd Parts Distinct

M. S. Mahadeva Naika and D. S. Gireesh
Department of Mathematics
Bangalore University
Central College Campus
Bangalore-560 001


Let pod-k(n) denote the number of partition k-tuples of n wherein odd parts are distinct (and even parts are unrestricted). We establish some interesting infinite families of congruences and internal congruences modulo 4, 16, and 5 for pod-2(n), pod-4(n), and pod-6(n), respectively. We also find Ramanujan-type congruences modulo 5 for pod-3(n) and densities of pod-2(n), pod-3(n), pod-4(n), and pod-6(n) modulo 4, 5, 16, and 5, respectively.

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(Concerned with sequences A006950 A273225 A273226 A273228 A273236.)

Received November 4 2015; revised version received April 18 2016; May 28 2016. Published in Journal of Integer Sequences, June 4 2016.

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