6 problems

Banks–Martin conjecture analogue. For each $q\geq 5$, the inequalities

Let $U(z)$ and $d6d1_1(z)$ be the functions defined in the paper for $z\in(0,2)$. Equality conjecture. … This is one of the paper's open questions concerning the relationship betwe…

Let $\Omega(n)$ be the number of prime factors of $n$, counted with multiplicity, and let $\mathbb{N}_k=\{n:\Omega(n)=k\}$. For a set of odd primes $\mathcal Q$, write…

For $x\ge 1$, let $[x,\infty)$ denote the integers at least $x$, and let $f(A)=\sum_{a\in A}1/(a\log a)$ for a primitive set $A$. Erdős–Sárközy–Szemerédi conjecture. … This questio…

Banks–Martin conjecture. The sequence of sums is strictly decreasing:

Let $A\subset \mathbb{Z}_{>1}$ be a primitive set, meaning that no member of $A$ divides another, and let … Let $\mathcal P$ denote the set of primes. Erdős's primitive set conject…