6 problems

Conjecture. $M'_{\mathrm{even}}(d)\leq 2$ if and only if $d\in\{2,6,10,14,22,26,30,38,42,62,110,122,182,278,362,398\}$.

Let $d otfor all?$.

Let $d otfor all?$.

Let $f$ be the Collatz function and let $\{f^{s}(a)\}_{s=1}^{\infty}$ be the corresponding Collatz process. Let $\Omega(a)$ denote the total number of prime factors of $a$, counted…

Prime factorization conjecture for factorials plus one. For every $n\in\mathbb N\setminus S$, the number $n!+1$ is square-free.

Let $q$ be the parameter defining the set $M^c(q)$, let $d(q)$ denote the density associated with this set, and let $I(n)$ be the indicator function of the event $n\in M^c(q)$. Def…