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

摘要

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.