Infinitely many composites n with n+1 dividing σ(n+1)

Determine whether there exist infinitely many positive composite integers n such that n+1 divides σ(n+1), where σ(·) denotes the sum-of-divisors function.

Background

The paper investigates divisibility conditions related to σ(n) and constructs a composite example n=20 with σ(n)=2(n+1). After establishing uniqueness of a particular form (n=p^2q with k=2) leading to n=20, the authors pose a broader question about the frequency of such phenomena, explicitly asking about n+1 dividing σ(n+1).