MathDB
Expression with d(n)

Source: Baltic Way 2009

November 27, 2010
number theory proposednumber theory

Problem Statement

Let d(k)d(k) denote the number of positive divisors of a positive integer kk. Prove that there exist in finitely many positive integers MM that cannot be written as M=(2nd(n))2M=\left(\frac{2\sqrt{n}}{d(n)}\right)^2 for any positive integer nn.