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(Jeffrey C. Lagarias) The following is equivalent to RH. Let $H_n = \sum\limits_{j=1}^n \frac{1}{j}$ be the $n$-th harmonic number. For each $n \ge 1$ $$\sum\limits_{d|n} d \le H_n + \exp (H_n) \log (H_n),$$ with equality only for $n = 1.$ (An Elementary Problem Equivalent to the Riemann Hypothesis. See also OEIS A057641.)

(Jeffrey C. Lagarias) The following is equivalent to RH. Let $H_n = \sum\limits_{j=1}^n \frac{1}{j}$ be the $n$-th harmonic number. For each $n \ge 1$ $$\sum\limits_{d\mid n} d \le H_n + \exp (H_n) \log (H_n),$$ with equality only for $n = 1.$ (An Elementary Problem Equivalent to the Riemann Hypothesis. See also OEIS A057641.)

(Jeffrey C. Lagarias) The following is equivalent to RH. Let $H_n = \sum\limits_{j=1}^n \frac{1}{j}$ be the $n$-th harmonic number. For each $n \ge 1$ $$\sum\limits_{d|n} d \le H_n + \exp (H_n) \log (H_n),$$ with equality only for $n = 1.$ (An Elementary Problem Equivalent to the Riemann Hypothesis. See also OEIS A057641.)

(Jeffrey C. Lagarias) The following is equivalent to RH. Let $H_n = \sum\limits_{j=1}^n \frac{1}{j}$ be the $n$-th harmonic number. For each $n \ge 1$ $$\sum\limits_{d|n} d \le H_n + \exp (H_n) \log (H_n),$$ with equality only for $n = 1.$ (An Elementary Problem Equivalent to the Riemann Hypothesis. See also OEIS A057641.)

(Jeffrey C. Lagarias) Assume RH. Let $H_n = \sum\limits_{j=1}^n \frac{1}{j}$ be the $n$-th harmonic number. For each $n \ge 1$ $$\sum\limits_{d|n} d \le H_n + \exp (H_n) \log (H_n),$$ with equality only for $n = 1.$ (An Elementary Problem Equivalent to the Riemann Hypothesis. See also OEIS A057641.)

(Jeffrey C. Lagarias) The following is equivalent to RH. Let $H_n = \sum\limits_{j=1}^n \frac{1}{j}$ be the $n$-th harmonic number. For each $n \ge 1$ $$\sum\limits_{d|n} d \le H_n + \exp (H_n) \log (H_n),$$ with equality only for $n = 1.$ (An Elementary Problem Equivalent to the Riemann Hypothesis. See also OEIS A057641.)