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Find all positive integers with exactly 16 positive divisors

Source: JBMO 2002, Problem 3

October 30, 2005
number theory proposednumber theory

Problem Statement

Find all positive integers which have exactly 16 positive divisors 1=d1<d2<…<d16=n1 = d_1 < d_2 < \ldots < d_{16} =n such that the divisor dkd_k, where k=d5k = d_5, equals (d2+d4)d6(d_2 + d_4) d_6.
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