6, 28, and 496 are the first three examples of, for 10 points, what type of number that equals the sum of its proper divisors?
With the exception of the smallest of their kind, all known examples of these can be expressed as the sum of cubes of consecutive odd numbers. Euler proved that there is a one-to-one correspondence between Mersenne primes and even types of this number, and they form a subset of the triangular numbers. Numbers which do not fit this category are classified as deficient or abundant, and these numbers all yield 2n when they form the argument of the divisor function. It is unknown whether any odd ones exist. 6, 28, and 496 are the first three examples of, for 10 points, what type of number that equals the sum of its proper divisors?
With the exception of the smallest of their kind, all known examples of these can be expressed as the sum of cubes of consecutive odd numbers.
perfect number