MathDB

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.

Problem Statement