MathDB

19

Part of 2020 Baltic Way

Problems(1)

A rounded multiple of the divisor function divides the number itself

Source: Baltic Way 2020, Problem 19

11/14/2020
Denote by d(n)d(n) the number of positive divisors of a positive integer nn. Prove that there are infinitely many positive integers nn such that ⌊3⋅d(n)⌋\left\lfloor\sqrt{3}\cdot d(n)\right\rfloor divides nn.
number theorynumber theory proposeddivisor function