3 problems

Under the restricted factorization described in the source, assign a fractional order $\operatorname{ord}(p)$ or $\operatorname{ord}(l)$ recursively to primes $p$ and lucky numbers…

A lucky prime is a prime number that is also a lucky number. The first examples are $3,7,13,31,37,43,\dots$. Lucky-prime conjecture. There are infinitely many lucky primes. This is…

The lucky divisibility functions are defined by … where $\overset{*}{\omega}(n)$ counts distinct lucky divisors and $\overset{*}{\Omega}(n)$ counts them with their lucky order. Luc…