Which would be the most efficient way (in computational time) to compute tr(inv(H)), where H is a (dense) square matrix? In my particular problem I also have a LU decomposition of H already ...
Although I am also interested in the number of distinct prime factors (not counting multiplicity), today I use $\omega(m)$ to denote the number of (positive) prime factors (with multiplicity) of the ...
For a prime gap of length at least $n$, a trivial upper bound for its first occurrence is $N=n!$ or $N=lcm(2,\dots,n)$. A bit better is $N=p_1\cdots p_n$ where $p_k$ is the $k$th prime, as then ...