Problem

Source: Switzerland 2019, final round, problem 8

Tags: number theory, Divisibility, sum of divisors



An integer n2 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.