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A rounded multiple of the divisor function divides the number itself

Source: Baltic Way 2020, Problem 19

November 14, 2020
number theorynumber theory proposeddivisor function

Problem Statement

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.
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