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sequence with relative primes , pages of a book numbered 2 to 400

Source: Mexican Mathematical Olympiad 1994 OMM P4

July 29, 2018
number theoryInteger sequencerelatively prime

Problem Statement

A capricious mathematician writes a book with pages numbered from 22 to 400400. The pages are to be read in the following order. Take the last unread page (400400), then read (in the usual order) all pages which are not relatively prime to it and which have not been read before. Repeat until all pages are read. So, the order would be 2,4,5,...,400,3,7,9,...,399,...2, 4, 5, ... , 400, 3, 7, 9, ... , 399, .... What is the last page to be read?
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