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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 functionfor  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.

Connections Between Partitions and Divisors Related to the Parity of the Partition Function