MathDB

Number Theory Is Blessed by This Problem of Author of Imo 2021 P3

Source: Ukrainian Mathematical Olympiad 2023. Day 2, Problem 11.7

April 5, 2023

number theory

Problem Statement

For a positive integer

n

consider all its divisors

1 = d_1 < d_2 < \ldots < d_k = n

. For

2 \le i \le k-1

, let's call divisor

d_i

good, if

d_{i-1}d_{i+1}

isn't divisible by

d_i

. Find all

n

, such that the number of their good divisors is smaller than the number of their prime distinct divisors.
Proposed by Mykhailo Shtandenko