MathDB

Let A = {1,4,6, ...} be a set of natural numbers n for which n is the product of an even number of primes and n+1 is the product of an odd number of primes (taking into account the multiplicity of prime powers). Prove that the series of the reciprocals of the elements of A is divergent. In other words,

A=\{n|\lambda(n)=1

and

\lambda(n+1)=-1\}

, where

\lambda

is the liouville lambda function.

Problem Statement