Problem

Source: 2024 Turkey TST P8

Tags: number theory



For an integer n, σ(n) denotes the sum of postitive divisors of n. A sequence of positive integers (ai)i=0 with a0=1 is defined as follows: For each n>1, an is the smallest integer greater than 1 that satisfies σ(a0a1an1)|σ(a0a1an).Determine the number of divisors of 20242024 amongst the sequence.