4 problems

Let $n=2^k p^m$, where $p$ is an odd prime, and suppose that $n$ is 2-near perfect when … for distinct positive divisors $d_1,d_2$ of $n$. Finiteness conjecture. There are only fin…

Let a Kalita–Saikia near superperfect number mean a number that is both a Kalita–Saikia number and a near superperfect number. Nonexistence conjecture. There are no odd Kalita–Saik…

A positive integer $n$ is near-perfect if it is the sum of all its proper divisors except one proper divisor, called its redundant divisor. The number $n$ is even when it is divisi…

A positive integer $n$ is near-perfect if it is the sum of all its proper divisors except one proper divisor, called its redundant divisor. For a fixed integer $k\geq 1$, the redun…