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Rioplatense L-A 2022 #6

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December 13, 2022
number theory

Problem Statement

A sequence of numbers is platense if the first number is greater than 11, and an+1=anpna_{n+1}=\frac{a_n}{p_n} which pnp_n is the least prime divisor of ana_n, and the sequence ends if an=1a_n=1. For instance, the sequences 864,432,216,108,54,27,9,3,1864, 432,216,108,54,27,9,3,1 and 2022,1011,337,12022,1011,337,1 are both sequence platense. A sequence platense is cuboso if some term is a perfect cube greater than 11. For instance, the sequence 864864 is cuboso, because 27=3327=3^3, and the sequence 20222022 is not cuboso, because there is no perfect cube. Determine the number of sequences cuboso which the initial term is less than 20222022.
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