Quasiperfect Numbers

Reference:

• Wikipedia

def QuasiperfectNumbers.Quasiperfect (n : ℕ) : Prop

A number is quasiperfect if the sum of its divisors is equal to $2n + 1$.

Equations

• QuasiperfectNumbers.Quasiperfect n = ((ArithmeticFunction.sigma 1) n = 2 * n + 1)

theorem QuasiperfectNumbers.exists_quasiperfect : True ↔ ∃ (n : ℕ), Quasiperfect n

Quasiperfect Numbers Conjecture. Do quasiperfect numbers exist?