Mersennelike

Mersennelike refers to numbers that share a structural similarity with Mersenne numbers, which are numbers of the form $2^n - 1$. While Mersenne numbers specifically require the exponent $n$ to be prime for the number itself to potentially be a Mersenne prime, Mersennelike numbers relax this constraint or explore variations.

A common interpretation of Mersennelike numbers is $2^n - 1$ where $n$ is any positive integer, not necessarily prime. This broader definition includes all Mersenne numbers, but also numbers like $2^4 - 1 = 15$ and $2^6 - 1 = 63$, where the exponent is composite.

Another related concept involves altering the base or the subtraction. For instance, numbers of the form $b^n - 1$ for some base $b > 2$ could be considered Mersennelike. Alternatively, numbers like $2^n + 1$ (Fermat numbers) or other simple polynomial forms could also be seen as analogous in their mathematical construction and the study of their properties, such as primality. The investigation of Mersennelike numbers often stems from the desire to generalize the properties and prime-finding challenges associated with Mersenne numbers.