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15

Part of 2013 Iran Team Selection Test

Problems(1)

sequence with divisors

Source: Iran TST 3, Day 1, Problem 3

5/12/2013
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?
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