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各位数字之和的求和函数的不等式。我们证明，几个已知结果可以从Mohanty、Greenbury、Sarkany、Narayanan、Dingle、Ahnert和Louis在2023年论文中的一个定理推导出来，该论文的主要范围是基因型-表型映射中的最大突变稳健性。