MathDB

complexity inequality, no of factors in prime decomposition

Source: Tournament of Towns, Junior A-Level , Fall 2019 p1

April 20, 2020

inequalitiesnumber theoryprimenumber of divisorsprime factorizationfactorsDivisors

Problem Statement

Let us call the number of factors in the prime decomposition of an integer

n > 1

the complexity of

n

. For example, complexity of numbers

4

and

6

is equal to

2

. Find all

n

such that all integers between

n

and

2n

have complexity a) not greater than the complexity of

n

. b) less than the complexity of

n

.
(Boris Frenkin)