Abstract
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/(7log log n). Our proof uses the first term of Rademacher’s formula for p(n).
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References
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This paper was written while the author was in sabbatical from the Mathematical Institute UNAM from January 1 to June 30, 2011 and supported by a PASPA fellowship from DGAPA.
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Luca, F. On the number of nonzero digits of the partition function. Arch. Math. 98, 235–240 (2012). https://doi.org/10.1007/s00013-011-0350-2
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DOI: https://doi.org/10.1007/s00013-011-0350-2