MathDB
sequence with divisors

Source: Iran TST 3, Day 1, Problem 3

May 12, 2013
number theory proposednumber theory

Problem Statement

a) Does there exist a sequence a1<a2<…a_1<a_2<\dots of positive integers, such that there is a positive integer NN that ∀m>N\forall m>N, ama_m has exactly d(m)−1d(m)-1 divisors among aia_is?
b) Does there exist a sequence a1<a2<…a_1<a_2<\dots of positive integers, such that there is a positive integer NN that ∀m>N\forall m>N, ama_m has exactly d(m)+1d(m)+1 divisors among aia_is?
Back to ProblemsView on AoPS