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omega(n) is the number of prime divisors of n

Source: ILL 1979 - Problem 78.

June 5, 2011
inequalitiesnumber theory unsolvednumber theory

Problem Statement

Denote the number of different prime divisors of the number nn by ω(n)\omega (n), where nn is an integer greater than 11. Prove that there exist infinitely many numbers nn for which ω(n)<ω(n+1)<ω(n+2)\omega (n)< \omega (n+1)<\omega (n+2) holds.
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