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).
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机译:令p(n)为计算n的分区数的函数。令b≥2为固定的正整数。在本文中,我们表明,对于几乎所有n,基数b中p(n)的位数之和至少为log n /(7 log log n)。我们的证明对p(n)使用Rademacher公式的第一项。
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