ON THE NUMBER OF DIVISORS OF A NUMBER AND THEIR SUM

John A. Ewell (U. S. A.)

Abstract

For given integers m, n, if then denotes the number of positive divisors of n and denotes the sum of the positive divisors of n. If then denotes the number of partitions of n into distinct odd parts; conventionally If and then denotes the number of partitions of n into parts not exceeding m; conventionally In this paper the functions d and s are expressed essentially in terms of the functions and

Keywords and phrases: expression of the divisor function and the sum-of-divisors function in terms of certain restricted partition functions.