On the number of nonzero digits of the partition function

摘要

Let p(n) be the function that counts the number of partitions of n. Let b ≥ 2 be a fixed positive integer. In this paper, we show that for almost all n the sum of the digits of p(n) in base b is at least log n/(7 log log n). Our proof uses the first term of Rademacher's formula for p(n).