MathDB
Putnam 1976 B6

Source:

April 20, 2022
college contests

Problem Statement

As usual, let σ(N)\sigma (N) denote the sum of all the (positive integral) divisors of N.N. (Included among these divisors are 11 and NN itself.) For example, if pp is a prime, then σ(p)=p+1.\sigma (p)=p+1. Motivated by the notion of a "perfect" number, a positive integer NN is called "quasiperfect" if σ(N)=2N+1.\sigma (N) =2N+1. Prove that every quasiperfect number is the square of an odd integer.