ON A RELATION BETWEEN THE SUM-OF-DIVISORS FUNCTION AND A RESTRICTED PARTITION FUNCTION
For a given integer n, if then denotes the sum of all positive divisors of n; denotes the exponent of the largest power of 2 dividing n; and then If then denotes the number of partitions of n into distinct parts, where conventionally In view of a known recurrence for this paper shows that recursive determination of entails that of the composite function
recursive determination of the sum-of-divisors function in terms of recursive determination of a certain restricted partition function.