On the sum of digits of the factorial
Number Theory
2014-10-30 v1
Abstract
Let b > 1 be an integer and denote by s_b(m) the sum of the digits of the positive integer m when is written in base b. We prove that s_b(n!) > C_b log n log log log n for each integer n > e, where C_b is a positive constant depending only on b. This improves of a factor log log log n a previous lower bound for s_b(n!) given by Luca. We prove also the same inequality but with n! replaced by the least common multiple of 1,2,...,n.
Keywords
Cite
@article{arxiv.1409.4912,
title = {On the sum of digits of the factorial},
author = {Carlo Sanna},
journal= {arXiv preprint arXiv:1409.4912},
year = {2014}
}
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4 pages