For given integers m, n, if n > 0, then d(n) denotes the number of positive divisors of n. If n ? 0, then q(n) denotes the number of partitions of n into distinct parts, where q(0) := 1. If m >0 and n ? 0, then p_m(n) denotes the number of partitions of n into parts not exceeding m; conventionally p_m (0) :=1. In this paper the function d(×¼/span>)is expressed in terms of the functions q(×¼/span>) and p_m (×¼/span>), m > 0.

expression of the divisor function in terms of certain restricted partition functions.