We revisit and generalize inequalities for the summatory function of the sum of digits in a given integer base. We prove that several known results can be deduced from a theorem in a 2023 paper by Mohanty, Greenbury, Sarkany, Narayanan, Dingle, Ahnert, and Louis, whose primary scope is the maximum mutational robustness in genotype-phenotype maps.

翻译：我们重新审视并推广了关于给定整数进制下数字求和函数的求和不等式。我们证明，若干已知结果可以从 Mohanty、Greenbury、Sarkany、Narayanan、Dingle、Ahnert 和 Louis 在2023年一篇论文中的定理推导得出，该论文的主要研究范围是基因型-表型图谱中的最大突变稳健性。