Abstract
Summary In this paper, the author gives two linear homogeneous recurrence relations to compute the values of Euler’s partition function p(n) when n is odd. These recurrences do not involve the generalized pentagonal numbers and provide new connections between the partition function p(n) and the positive divisor function for x = 0 and x = 1. Some relations involving the divisor functions . and the parity of the partition function p(n) are presented in this context.
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