List questions from harmonic-numbers

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On integer sequences of the form $\sum_{n=1}^N (a(n))^2H_n^2,$ where $H_n$ is the $n$th harmonic number: refute my conjecture and add yourself example

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A Gift Problem for the Year 2018

Hypergeometric series with harmonic factor

Infinite series with harmonic numbers related to elliptic integrals

A non obvious example of a sequence $a(k)\cdot H_{b(k)}$ whose general term is integer many times, where $H_n$ denotes the $n$th harmonic number

On integer sequences of the form $\sum_{n=1}^N (a(n))^2H_n^2,$ where $H_n$ is the $n$th harmonic number: refute my conjecture and add yourself example

Simple formula for $H_n = m + \alpha $?

Limit of the difference between two harmonic numbers

Justify an approximation of $-\sum_{n=2}^\infty H_n\left(\frac{1}{\zeta(n)}-1\right)$, where $H_n$ denotes the $n$th harmonic number

Show that for $n\gt 2$, $\frac{\sigma_1(n)}{n}\lt H_n$

first derivative of exponential generating function of harmonic numbers

Calculating the summation $\sum_{n=1}^{\infty}\frac{H_{n+1}}{n(n+1)}$

Binomial Harmonic Numbers

Derivative of binomial coefficients

Series involving product of Harmonic Numbers

Asymptotics of product of harmonic numbers

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