2 problems

Let … where the product runs over all prime powers unitarily dividing $N$; this is the unitary totient of $N$. Subbarao's conjecture. … if and only if $N$ is a prime power. This is…

Let $\sigma^+(n)$ denote the sum of the unitary positive divisors of the positive integer $n$. The conjecture on $\sigma^+$ values. For each prime $q\geq 3$, there exist infinitely…