2 problems

For real $a>0$, let $\Omega(n)$ denote the number of prime factors of $n$, counting multiplicity, and define … For $a\geq 2$, the function has jumps of size $x^{\log a/\log 2}$ at…

Let $a$, $b$, $c$, and $k$ be positive integers such that $1\leq a\leq b$, $a<c<2(a+b)$, $c\ne b$, and $(a,b,c)=1$. Define the arithmetic function $f_k(a,b;c;n)$ by … and its summa…