Problem

Source: Switzerland 2019, final round, problem 8

Tags: number theory, Divisibility, sum of divisors



An integer $n\ge2$ is called resistant, if it is coprime to the sum of all its divisors (including $1$ and $n$). Determine the maximum number of consecutive resistant numbers. For instance: * $n=5$ has sum of divisors $S=6$ and hence is resistant. * $n=6$ has sum of divisors $S=12$ and hence is not resistant. * $n=8$ has sum of divisors $S=15$ and hence is resistant. * $n=18$ has sum of divisors $S=39$ and hence is not resistant.