TWO RESULTS ABOUT THE SUM-OF-DIVISORS FUNCTION
For each integer denotes the sum of all positive divisors of n; denotes the exponent of the largest power of 2 dividing n, and then For each integer denotes the number of partitions of n into distinct parts; and, denotes the number of partitions of n into distinct odd parts. Conventionally, It is here demonstrated in four different ways that the composite function can be expressed additively in terms of the functions
expression of the sum-of-divisors function in terms of certain restricted partition functions.