Mersenne-prime conjecture for odd redundant divisors

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 divisible by $2$, and a Mersenne prime is a prime of the form $2^p-1$ with $p$ prime. Mersenne-prime conjecture. If an even near-perfect number has an odd redundant divisor, then that redundant divisor is a Mersenne prime. This is presented as a conjecture and is used later as one of the hypotheses for an Euler-like theorem.