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w(n) < w(n + 1) < w(n + 2), no of different primes that divide n

Source: 2015 Latvia BW TST P15

December 16, 2022
number theoryDivisorsprime divisorprime divisors

Problem Statement

Let w(n)w (n) denote the number of different prime numbers by which nn is divisible. Prove that there are infinitely many natural numbers nn such that w(n)<w(n+1)<w(n+2)w(n) < w(n + 1) < w(n + 2).
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