SOME IDENTITIES CONCERNING PARTITION FUNCTIONS AND DIVISOR SUMS
Let n, r μ/span> N, with r ? 2. Consider the partition functions q0(n), br(n), pr(n), which denote respectively the number of partitions of n into distinct odd parts, parts not divisible by r, parts in r distinct colors. We obtain explicit formulas for each of these partition functions in terms of s(n) (the usual sum-of-divisors function) or s(r)(n) (the sum of the divisors of n that are not multiples of r).
partitions, divisor sums.
