For ten points, identify this type of thus-far undiscovered number, which equals the sum of its divisors and is not divisble by two.
Any number of this type must have the form n equals 12 m plus 1 or n equals 36 m + 9, for integer m, according to a theorem by Jacques Touchard. They would have the form a squared times quantity 4 b plus 1 raised to the power 4 c plus 1, a result demonstrated by Euler. These numbers do not exist if Ore's conjecture is true, and if one does exist, the work of Brent, Cohen, and Riele indicates that it must be greater than 10 to the 300 power. Arguments against the existence of these numbers include Sylvester's web of conditions and the Pomerance heuristic, and unlike a similar type of number, they do not correspond to Mersenne primes. For ten points, identify this type of thus-far undiscovered number, which equals the sum of its divisors and is not divisble by two.
Any number of this type must have the form n equals 12 m plus 1 or n equals 36 m + 9, for integer m, according to a theorem by Jacques Touchard.
{odd perfect} number