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Congruences modulo powers of 2 for a certain partition function

Authors:	Hei-Chi Chan Shaun Cooper

Affiliation:	(3) Department of Mathematics and Computer Science, Babeş-Bolyai University of Cluj, Cluj-Napoca, Romania;(4) formerly the Technical University of Timişoara, Timişoara, Romania;

Abstract:	We study the divisibility properties of the coefficients c(n) defined by $prod_{n=1}^inftyfrac{1}{(1-q^n)^2(1-q^{3n})^2}=sum _{n=0}^infty c(n)q^n.$ An analogue of Ramanujan’s partition congruences is obtained for certain coefficients c(n) modulo powers of 2. Furthermore, an analogue of the identity that Hardy regarded as Ramanujan’s most beautiful is proved.

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