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Part of 2014 Rioplatense Mathematical Olympiad, Level 3

Problems(1)

unusual property of some numbers with 8 divisors (i.e. 2014)

Source: Rioplatense Olympiad 2014 level 3 P2

9/5/2018
El Chapulín observed that the number 20142014 has an unusual property. By placing its eight positive divisors in increasing order, the fifth divisor is equal to three times the third minus 44. A number of eight divisors with this unusual property is called the red number . How many red numbers smaller than 20142014 exist?
number theorynumber of divisorsDivisors